Question

Given the following diagram, find the missing measure.*​

Answer 1

Option C:

x = 30

Solution:

The given image is a triangle.

angle 1, angle 2 and angle 3 are interior angles of a triangle.

angle 4 is the exterior angle of a triangle.

m∠4 = 2x°, $m\angle2=\frac{4}{3}x^\circ$, m∠3 = 20°

Exterior angle theorem:

In triangle, the measure of exterior angle is equal to the sum of the opposite interior angles.

By this theorem,

m∠4 = m∠2 + m∠3

$2x^\circ=\frac{4}{3}x^\circ+20^\circ$

Subtract $\frac{4}{3}x^\circ$ on both sides of the equation.

$2x^\circ-\frac{4}{3}x^\circ=20^\circ$

To make the denominator same and then subtract.

$\frac{6}{3}x^\circ -\frac{4}{3}x^\circ=20^\circ$

$\frac{2}{3}x^\circ =20^\circ$

Multiply by $\frac{3}{2}$ on both sides of the equation.

x° = 30°

x = 30

Hence option C is the correct answer.