Answer:
The value of x is 10
Step-by-step explanation:
<em>The measure of the </em><em>exterior angle at one vertex</em><em> of a triangle equals </em><em>the sum of the measures of the two opposite interior angles </em><em>to this vertex.</em>
In ΔNOP
∵ ∠OPQ is an exterior angle of the triangle at vertex P
∵ ∠PNO and ∠NOP are the opposite interior angles of vertex P
→ By using the rule above
∴ m∠OPQ = m∠PNO + m∠NOP
∵ m∠OPQ = (6x - 15)°
∵ m∠PNO = (2x + 18)°
∵ m∠NOP = (2x - 13)°
→ Substitute them in the equation above
∴ 6x - 15 = 2x + 18 + 2x - 13
→ Add the like terms in the right side
∵ 6x - 15 = (2x + 2x) + (18 - 13)
∴ 6x - 15 = 4x + 5
→ Subtract 4x from both sides
∵ 6x - 4x - 15 = 4x - 4x + 5
∴ 2x - 15 = 5
→ Add 15 to both sides
∵ 2x - 15 + 15 = 5 + 15
∴ 2x = 20
→ Divide both sides by 2 to find x
∴ x = 10
∴ The value of x is 10
