Question

14.Find the value of <A in the following figure.
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Answer 1

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.