ACT Angle Questions

AB and CD are two parallel lines intersected by line EF. If the measure of angle 1 is 132°, what is the measure of angle 2?

• 24°

• 48°

• 64°

• 132°

• 180°

Answer explanation

Angle 1 and Angle 2 are corresponding angles, which means they are congruent (equal).

Tags

CCSS.8.G.A.5

Figure not drawn to scale.

In the figure above, APB forms a straight line. If the measure of angle APC is eighty-one degrees larger than the measure of angle DPB, and the measures of angles CPD and DPB are equal, then what is the measure, in degrees, of angle CPB?

• 33

• 40

• 50

• 66

• 114

Answer explanation

APC is eighty-one degrees larger than the measure of angle DPB so we will label DPB as x + 81 and APC as x.

The measures of angles CPD and DPB are equal so CPD is also x.

So x+81+x+x=180, solve for x.

3x+81=180

3x=99

x=33

Find the measure of angle CPB:

CPB is x+x so 33 + 33 = 66

Tags

CCSS.7.G.B.5

In the diagram, AB || CD. What is the value of a+b?

• 60°

• 80°

• 140°

• 160°

• None of the other answers.

Answer explanation

b = 20 because vertical angles are congruent.

a = 140 because a is across from the same side interior angle of 40 (supplementary to 40)

So a + b is 20 + 140 = 160

Two pairs of parallel lines intersect. If A = 135°, what is 2*|B-C| = ?

• 140°

• 150°

• 160°

• 170°

• 180°

Answer explanation

A is 135, the corresponding angle (next to B) is also 135.

B is 180 - 135 = 45

C is a same side interior angle of B, so it is 180 - 45 = 135

2*|B-C| = 2*|45-135| = 2*|-90| = 180

Tags

CCSS.8.G.A.5

• 5°
• 10°

• 15°

• 30°

• 40°

Answer explanation

Draw a diagram, ABC is 20 and an angle bisector splits and angle into 2 equal pieces so EBC and DBE are both 20.

BE further bisects DBC so DBE and EBC are both 5.

ABE is ABD + DBE so 10 + 5 = 15

Tags

CCSS.HSG.CO.C.9

What is the value of x in the figure above?

• 50°

• 54°

• 108°

• 120°

• 155°

Answer explanation

The sum of interior angles in a triangle is 180

The sum of interior angles in a quadrilateral (like a square) is 360.

The sum of interior angles in a pentagon is 540.

(sum of interior angles increases by 180 for each additional side).

Find the interior angles, then add them up and set them equal to 540 to solve for x.

Points A, B, C, D are collinear. The measure of ∠DCE is 130° and of ∠AEC is 80°. Find the measure of ∠EAD.

• 50°

• 40°

• 60°

• 70°

Answer explanation

Since DCE is 130, the angle next to is (BCE) is 180 - 130 = 50

Ignore line EB and look at the larger triangle, the top angle is 80 and the right angle is 130 so:

80 + 50 + x = 180

130 + x = 180

x = 50

So angle EAD is 50 degrees

Tags

CCSS.7.G.B.5

In the figure shown below, the measure of ∠SRT is (x + 15)° and the measure of ∠SRU is 90°. What is the measure of ∠TRU?

• (105 + x)°

• (105 − x)°

• (75 + x)°

• (75 − x)°

• (x − 75)°

Answer explanation

Since ∠SRU is 90°, ∠SRT + ∠TRU = 90

Since ∠SRT is (x + 15)°, ∠TRU is 90 - (x + 15)°

This simplifies to (75 - x)°.

Tags

CCSS.7.G.B.5

The isosceles triangle below has one angle measure as shown. What is the measure of each of the other angles?

• 30°

• 45°

• 50°

• 65°

• 130°

Answer explanation

An isosceles triangle has 2 congruent sides and 2 congruent angles.

Since the top angle is 50 and the sum of the angles in a triangle is 180, 180 - 50 = 130 degrees remaining for the two remaining angles.

130/2 (since the 2 remaining angles are equal) = 65.

Tags

CCSS.8.G.A.5

In the circle shown below, C is the center and lies on segments AE and BF. Which of the following statements is NOT true?

• ∠BAC measures 70°

• AB is parallel to EF

• AB ≅ BD

• ∠BCE ≅ ∠DCF

• CF ≅ EF

Answer explanation

You are looking for the statement that is NOT true.

A: 180 - 40 = 140/2 (2 congruent angles) = 70. This is true.

B: AB and FE are on opposite sides of the circle in the same position so they are parallel.

C: Triangle ABC and BCD are congruent (same size) so AB is congruent (equal) to BD.

D: Angle BCE is 40 + angle DCE and angle DCF is angle DCE + 40 so they are congruent.

E: Only remaining answer so it must be false. CF is the radius of the circle while EF is a segment along the circumference, they are NOT equal.

Tags

CCSS.HSG.C.A.2