The Triangle and Its Properties — Practice

Question 1

Two angles of a triangle are 40 and 75 degrees. Find the third angle.

Accepted Answer

Third angle = 180 - (40 + 75) = 180 - 115 = 65 degrees.

Question 2

In a right triangle, the two legs are 6 cm and 8 cm. Find the hypotenuse.

Accepted Answer

hypotenuse^2 = 6^2 + 8^2 = 36 + 64 = 100. Hypotenuse = sqrt(100) = 10 cm.

Question 3

The exterior angle of a triangle is 110 degrees and one opposite interior angle is 60 degrees. Find the other opposite interior angle.

Accepted Answer

Exterior angle = sum of opposite interior angles. 110 = 60 + other -> other = 50 degrees.

Question 4

In an isosceles triangle, the vertex angle is 50 degrees. Find the base angles.

Accepted Answer

Base angles are equal. 2x + 50 = 180 -> 2x = 130 -> x = 65. Each base angle is 65 degrees.

Question 5

In triangle PQR, angle P = 2x, angle Q = 3x, angle R = 5x. Find all angles.

Accepted Answer

2x + 3x + 5x = 180 -> 10x = 180 -> x = 18. So P = 36, Q = 54, R = 90 degrees (a right triangle).

Practice — The Triangle and Its Properties