14.Find the value of <A in the following figure.

Question

asked Oct 13, 2022 108k views

1 Answer

Sushruth · Answer 1 · 2022-10-16T14:57:07+0000

Given:

The figure of triangle ABC.

To find:

The measure of angle A.

Solution:

From the given figure, we get

$\angle ABC+120^\circ=180^\circ$ (Linear pair)

$\angle ABC=180^\circ-120^\circ$

$\angle ABC=60^\circ$

According to the exterior angle theorem, the exterior angle of a triangle is equal to the sum of two opposite interior angles.

$\angle A+\angle ABC=105^\circ$ (Exterior angle theorem)

$\angle A+60^\circ=105^\circ$

$\angle A=105^\circ-60^\circ$

$\angle A=45^\circ$

Therefore, the measure of angle A is 45 degrees.