Question

12. An exterior angle of a triangle is 105º and
its interior opposite angles are equal to each
other. Find the measure of each angle of the
triangle​

Answer 1

Given:

• An exterior angle of triangle is 105°
• Interior opposite angles are equal to each other.

To Find:

• Measure of all the angles of the triangle.

Solution:

Exterior angle is equal to the sum of opposite enterior angles.

• let the equal angles be x
• let the remaining angle = y

⟹x + x = 105

⟹2x = 105

⟹x = 105/2

⟹x = 52.5

so, the measure of equal angles is 52.5

[ sum of all angles of a triangle is 180°]

⟹x + x + y = 180°

⟹52.5 + 52.5 + y = 180°

⟹105 + y = 180°

⟹y = 180 - 105

⟹y = 75°

The angles of triangle : 75°, 52.5 and 52.5