Q5 of 34 Page 113

In the adjacent triangle ABC, find the value of x and calculate the measure of all the angles of the triangle.

Given:

∠A = x + 15, ∠B = x - 15, ∠ C = x + 30



As we know, using theorem (1), in any triangle, sum of the three interior angles is 180°.


So,


∠A + ∠B + ∠ C = 180°


⇒ x +15 + x – 15 + x + 30 = 180°


⇒ 3x + 30° = 180°


⇒ 3x = 180° - 30°


⇒ 3x = 150°


⇒ x = 50°


So, the angles are,


∠A = x + 15 = 50° + 15° = 65°


∠B = x - 15 = 50° - 15° = 35°


∠ C = x + 30 = 50° + 30° = 80°


More from this chapter

All 34 →
3

If the vertex angle of an isosceles triangle is 50°, find the other angles.

 4

The angles of a triangle are in the ratio 1:2:3. Determine the three angles.

 6

The angles of a triangle are arranged in ascending order of their magnitude. If the difference between two consecutive angles is 10°, find the three angles.

 1

The exterior angles obtained on producing the base of a triangle both ways are 104° and 136°. Find the angles of the triangle.