Question

Find the value of x and measure of an exterior angle of the given Triangle.

Answer 1

Answer:

Solution is in the above attached sheet

Answer 2

Answer :

x = 25°

Measure of the exterior angle = 65°

Explanation :

How to find ?

→ Let's find x first by the angle sum property of triangle [ The measure of the exterior angle of a triangle is the sum of the two interior opposite angles ] . We shall use transposition method in finding x. When we find the measure of x, we can easily find the measure of the exterior angle.

Steps :

$25 + (x + 15) = 3x - 10 \\ \implies 25 + x + 15 = 3x - 10 \\ \implies 40 + x = 3x - 10 \\ \implies 40 + 10 = 3x - x \\ \implies 50 = 2x \\ \implies \frac{50}{2} = x \\ \implies 25 = x$

.°. x = 25°

Then,

The measure Exterior angle of the triangle

= 3x-10

= 3 × 25° - 10

= 75° - 10

= 65°

Hence, x = 25° & the measure of the exterior angle = 65°.

$\rm\blue{So,done!}$