Add Segments
Find the length of segment AB if A-C-B, AC = 3 cm, and CB = 7 cm.
AB=10
What is the sum of the interior angles of any triangle?
1800
If m∠A = 35° and m∠B = 45°. What is m∠A + m∠B?
800
Define an isosceles triangle.
A triangle with two congruent sides.
OR
A triangle with two congruent angles.
Lines intersect, forming a 115 ° angle. What are the measures of the other three angles?
1150, 650, 650
If AB = 12, BC = 5, and AC is the entire segment from A to C passing through B, find AC.
AC=17
Two angles are complementary. If one angle is 30°, what is the other?
900
Two angles measure 2x + 10 and 3x − 5. Their sum is 125°. Solve for x and give both angle measures.
x=24; 580, 670
In triangle ABC, m∠A = 50°, m∠B = 60°. Find m∠C.
700
Base angles of an isosceles triangle are (3x + 5)° and (2x + 20)°. Find x and all angle measures.
x=150, 500, 500, 800
On a number line, point P is at -2, and Q is at 5. What is the length of segment PQ?
PQ=7
— 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
In triangle ABC, m∠A + m∠B = 110°. Find m∠C.
700
Base angles of an isosceles triangle are (3x + 5)° and (2x + 20)°. Find x and all angle measures.
150; 500, 500, 800
The angles of a triangle are in the ratio 2:3:4. Find each angle measure.
x=200; 400, 600, 800
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
An angle is 20° more than its supplement.
1000, 800
Two adjacent angles form a straight line. If their measures are (4x − 35)° and (3x + 5)°, find x and both angles.
300; 850,950
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
Angles are complementary. One is 4 times the other. Find the measures.
180, 720
Two segments have lengths in the ratio 5:7. Their sum is 96 cm. Find each segment length.
x=8, 40, 56
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'
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=20o, 400, 650, 750
In an isosceles triangle, the vertex angle is 30° less than each base angle. Find all angles.
x=400; 700, 700
The difference between the two collinear segment lengths is 14. Their sum is 86. Find both lengths.
50, 36