Final Review I Segments. Angles. Triangles

Add Segments

100

Find the length of segment AB if A-C-B, AC = 3 cm, and CB = 7 cm.

AB=10

200

If AB = 12, BC = 5, and AC is the entire segment from A to C passing through B, find AC.

AC=17

300

On a number line, point P is at -2, and Q is at 5. What is the length of segment PQ?

PQ=7

400

Points A, C, and B are collinear in this order with AB = 4x, BC = 3x − 2, and AC = 25. Solve for x, then find AB.

x=25, AB=100

500

Two segments have lengths in the ratio 5:7. Their sum is 96 cm. Find each segment length.

x=8, 40, 56

Sum of Angles in a Triangle. Complementary/Supplementary Angles

100

What is the sum of the interior angles of any triangle?

180⁰

200

Two angles are complementary. If one angle is 30°, what is the other?

90⁰

300

— In triangle ABC, m∠A − m∠B = 12° and m∠A + m∠B = 120°. Find m∠A and m∠B.

A=66⁰, b=54⁰, C=60⁰

400

An angle is 20° more than its supplement.

100⁰, 80⁰

500

If angle A is (3x + 20)° and angle B is (5x − 10)° and they are supplementary, find x and the angles. Provide the answer in degrees and minutes. 

21⁰15', 41⁰ 15' 

Sum of Angles

100

If m∠A = 35° and m∠B = 45°. What is m∠A + m∠B?

80⁰

200

Two angles measure 2x + 10 and 3x − 5. Their sum is 125°. Solve for x and give both angle measures.

x=24; 58⁰, 67⁰

300

In triangle ABC, m∠A + m∠B = 110°. Find m∠C.

70⁰

400

Two adjacent angles form a straight line. If their measures are (4x − 35)° and (3x + 5)°, find x and both angles.

30⁰; 85⁰,95⁰

500

Angles in a polygon are grouped; given three angles 2x, 3x + 5, and 4x − 5 sum to 180°, solve for x and each angle.

x=20^o, 40⁰, 65⁰, 75⁰

Isosceles Triangle

100

Define an isosceles triangle. 

A triangle with two congruent sides.

OR

A triangle with two congruent angles.

200

In triangle ABC, m∠A = 50°, m∠B = 60°. Find m∠C.

70⁰

300

Base angles of an isosceles triangle are (3x + 5)° and (2x + 20)°. Find x and all angle measures.

15⁰_; 50⁰, 50⁰, 80⁰

400

One angle of a triangle is twice the second, and the third angle is three times the second. Find all angles.

x=30⁰, 60⁰, 90⁰

500

In an isosceles triangle, the vertex angle is 30° less than each base angle. Find all angles.

x=40⁰; 70⁰, 70⁰

Miscellaneous

100

Lines intersect, forming a 115 ° angle. What are the measures of the other three angles?

115⁰, 65⁰, 65⁰

200

Base angles of an isosceles triangle are (3x + 5)° and (2x + 20)°. Find x and all angle measures.

x=15⁰, 50⁰, 50⁰, 80⁰

300

The angles of a triangle are in the ratio 2:3:4. Find each angle measure.

x=20⁰; 40⁰, 60⁰, 80⁰

400

Angles are complementary. One is 4 times the other. Find the measures.

18⁰, 72⁰

500

The difference between the two collinear segment lengths is 14. Their sum is 86. Find both lengths.

50, 36