Question

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Answer 1

Answer:

The value of x is 10

Step-by-step explanation:

The measure of the exterior angle at one vertex of a triangle equals the sum of the measures of the two opposite interior angles to this vertex.

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