Answer:
The value of x is 5
Step-by-step explanation:
<em>The measure of the </em><em>exterior angle</em><em> at one vertex of a triangle equals the </em><em>sum of the measures of the two opposite interior angles</em><em> to this vertex</em>
In ΔQRS
∵ ∠QRS is an exterior angle of the triangle at vertex R
∵ ∠PQR and ∠RPQ are the opposite interior angles of vertex R
→ By using the rule above
∴ m∠QRS = m∠PQR + m∠RPQ
∵ m∠QRS = (10x - 10)°
∵ m∠PQR = (2x + 1)°
∵ m∠RPQ = (3x + 14)°
→ Substitute them in the equation above
∴ 10x - 10 = 2x + 1 + 3x + 14
→ Add the like terms in the right side
∵ 10x - 10 = (2x + 3x) + (1 + 14)
∴ 10x - 10 = 5x + 15
→ Subtract 5x from both sides
∵ 10x - 5x - 10 = 5x - 5x + 15
∴ 5x - 10 = 15
→ Add 10 to both sides
∵ 5x - 10 + 10 = 15 + 10
∴ 5x = 25
→ Divide both sides by 5 to find x
∴ x = 5
∴ The value of x is 5
