In triangle ABC, the measure of angle A is 48^°, and the measure of angle B is 3 times the measure of angle C. What is the measure of angle C?

B. 33^°. The angles of a triangle sum to 180^°, so B + C = 180^° - 48^° = 132^°. Because B = 3C, substitute: 3C + C = 4C = 132^°. Divide by 4: C = 33^°.

ACT Math reporting category

ACT Geometry Practice

Geometry is the ACT math reporting category about shapes and space: angles, triangles, circles, solids, congruence and similarity, area and volume, right-triangle trigonometry, and coordinate geometry. According to ACT, it makes up 17–20% of scored math questions, as part of Preparing for Higher Math.

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17–20% of scored Math questions3 original questionsInstant answer checks

At a glance

Geometry on the ACT: the key numbers

Section and category facts from ACT.org, checked October 9, 2026. Time per question is ACT's section time divided by its question count.
Section	ACT Math: 45 questions in 50 minutes
Scored questions	41 scored, 4 field test
Reporting category	Geometry (part of Preparing for Higher Math)
Share of scored questions	17–20%, according to ACT
Average time per question	About 67 seconds
Counts toward the Composite	Yes
Practice on this page	3 original questions: Easy, Medium, Hard

What this tests

What does ACT Geometry test?

Angles and triangles. Use angle sums, angle pairs formed by parallel lines, and triangle properties to find missing measures.
Congruence and similarity. Set up proportions between corresponding sides of similar figures, and use congruence to find equal lengths and angles.
Area and volume. Find the perimeter, area, surface area, and volume of common shapes and solids, including figures built from several shapes.
Right-triangle trigonometry. Use the Pythagorean theorem and the sine, cosine, and tangent ratios to find missing sides and angles.
Circle properties. Work with radius, diameter, circumference, area, arcs, and the equation of a circle in the coordinate plane.
Coordinate geometry. Find distance, midpoint, and slope, and connect equations to lines and shapes in the $x y$ -plane.

Practice questions

Practice ACT Geometry questions

Pick an answer to check it. Each question has one correct choice.

Question 1 of 3Easy

In triangle

A B C

, the measure of angle

A

4 8^{\circ}

, and the measure of angle

B

is 3 times the measure of angle

C

. What is the measure of angle

C

Show answer and explanation

Correct answerB. $3 3^{\circ}$

How to solve it

The angles of a triangle sum to $18 0^{\circ}$ , so $B + C = 18 0^{\circ} - 4 8^{\circ} = 13 2^{\circ}$ .
Because $B = 3 C$ , substitute: $3 C + C = 4 C = 13 2^{\circ}$ .
Divide by 4: $C = 3 3^{\circ}$ .

Why the other choices miss

1 6^{\circ}

divides angle

A

by 3, which uses the wrong angle.

4 4^{\circ}

divides

13 2^{\circ}

by 3, forgetting that angle

C

adds a fourth part.

9 9^{\circ}

is the measure of angle

B

, not angle

C

Question 2 of 3Medium

In right triangle

A B C

, angle

C

is the right angle,

A C = 8

, and

B C = 6

. What is

sin A

Show answer and explanation

Correct answerA. $\frac{3}{5}$

How to solve it

Find the hypotenuse: $A B = 8^{2} + 6^{2} = 100 = 10$ .
Relative to angle $A$ , the opposite side is $B C = 6$ and the adjacent side is $A C = 8$ .
So $sin A = \frac{opposite}{hypotenuse} = \frac{6}{10} = \frac{3}{5}$ .

Why the other choices miss

\frac{3}{4}

tan A

, opposite over adjacent.

\frac{4}{5}

cos A

, which uses the adjacent side

A C

in place of the opposite side.

\frac{4}{3}

divides adjacent by opposite, flipping the tangent ratio.

Question 3 of 3Hard

A circle in the

x y

-plane has the equation

x^{2} + y^{2} - 6 x + 8 y = 11

. What is the radius of the circle?

Show answer and explanation

Correct answerC. $6$

How to solve it

Group the terms: $(x^{2} - 6 x) + (y^{2} + 8 y) = 11$ .
Complete each square by adding 9 and 16 to both sides: $(x - 3)^{2} + (y + 4)^{2} = 36$ .
The right side is $r^{2} = 36$ , so the radius is $6$ .

Why the other choices miss

11

completes the squares on the left but never adds 9 and 16 to the right side.

5

uses only

9 + 16 = 25

and drops the original 11.

36

r^{2}

, not the radius.

Avoid these traps

What mistakes do students make on Geometry?

Mixing up trig ratios

Students use the adjacent side for sine or flip the tangent ratio, especially when the named angle is not in the position they usually picture.

Fix: Label the opposite side, adjacent side, and hypotenuse relative to the named angle before writing any ratio.

Completing squares on one side

When rewriting a circle equation, students add the numbers that complete each square to the left side only.

Fix: Whatever you add to the left side, add to the right side in the same step.

Reporting the squared radius

In $(x - h)^{2} + (y - k)^{2} = r^{2}$ , students give the number on the right side as the radius.

Fix: Take the square root of the right side, and confirm that you are reporting $r$ , not $r^{2}$ .

Study method

How should you practice ACT Geometry?

Draw and label a sketch for every geometry problem, even when the question gives only text.
Write the formula you plan to use before you substitute any numbers.
Learn the angle sums, the Pythagorean theorem, and the sine, cosine, and tangent ratios well enough to write them quickly.
Check answers for reasonableness. For example, a leg of a right triangle cannot be longer than the hypotenuse.
Work Geometry sets in Dolphin, and note which shapes or formulas cause most of your misses.

Start ACT practice in Dolphin

FAQ

Questions about ACT Geometry

What does the ACT Geometry category cover?

It covers angles, triangles, circles, polygons, and solids, plus congruence and similarity, area and volume, right-triangle trigonometry, and coordinate geometry. The three questions on this page practice an angle sum, a sine ratio, and finding a radius from a circle equation.

How much of ACT math is Geometry?

According to ACT, Geometry makes up 17–20% of scored math questions. It is one of five areas that ACT groups under Preparing for Higher Math, along with Number & Quantity, Algebra, Functions, and Statistics & Probability. Together those five make up 80% of scored math questions.

Which geometry formulas should I study?

Focus on the ones you use most: the triangle angle sum, the Pythagorean theorem, area of triangles, rectangles, and circles, circumference, volume of prisms and cylinders, the distance and midpoint formulas, and the circle equation. Practice writing them from memory so you can apply them quickly.

What should I do when a geometry problem has no figure?

Draw a quick sketch from the text, label every given length and angle, and mark what you need to find. The questions on this page are written so that a sketch made from the words is enough to solve them.

How can I tell whether Geometry is a weak area for me?

Your ACT score report lists each reporting category with the number of questions in it, the number you answered correctly, and your percent correct. During practice, track your misses by topic, such as trig ratios, circles, or volume, to see where to focus.

Related practice

Sources

Where these facts come from

ACT: Understanding Your ACT Scores: reporting categories, category shares, Composite calculation, and scoring.
ACT: Test Enhancements and Changes: section length, question counts, and optional Science.
ACT: Official test preparation and free practice tests: released ACT questions in the real test format.

ACT facts checked October 9, 2026. Every practice question on this page is original Dolphin practice written to match one ACT reporting category. None is a released ACT item.

ACT® is a trademark registered by ACT, Inc., which is not affiliated with, and does not endorse, Dolphin.

ACT Geometry Practice

Geometry on the ACT: the key numbers

What does ACT Geometry test?

Practice ACT Geometry questions

How to solve it

How to solve it

How to solve it

What mistakes do students make on Geometry?

Mixing up trig ratios

Completing squares on one side

Reporting the squared radius

How should you practice ACT Geometry?

Questions about ACT Geometry

Keep practicing for the ACT

Where these facts come from