Question

Solve for x in the diagram below.

Answer 1

x = 25 °

Explanation:

First realize the opposite angles are equal , then

(4 x + 50)° = 150 °

x = 25 °

Answer 2

x = 25

Explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

From inspection of the given diagram, it appears that angle 150° and angle (4x + 50)° are opposite vertical angles.

Therefore, applying the Vertical Angle Theorem:

`\implies (4x+50)^(\circ)=150^(\circ)`

`\implies 4x+50=150`

`\implies 4x=100`

`\implies x=25`