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°, [tex]m\angle2=\frac{4}{3}x^\circ[/tex], 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
[tex]$2x^\circ=\frac{4}{3}x^\circ+20^\circ[/tex]
Subtract [tex]\frac{4}{3}x^\circ[/tex] on both sides of the equation.
[tex]$2x^\circ-\frac{4}{3}x^\circ=20^\circ[/tex]
To make the denominator same and then subtract.
[tex]$\frac{6}{3}x^\circ -\frac{4}{3}x^\circ=20^\circ[/tex]
[tex]$\frac{2}{3}x^\circ =20^\circ[/tex]
Multiply by [tex]\frac{3}{2}[/tex] on both sides of the equation.
x° = 30°
x = 30
Hence option C is the correct answer.
