Question

In ΔPQR, is extended through point R to point S, P, Q, R, equals, 3, x, plus, 13, right bracket, degreesm∠PQR=(3x+13) ∘ , m, angle, Q, R, S, equals, left bracket, 7, x, plus, 7, right bracket, degreesm∠QRS=(7x+7) ∘ , and m, angle, R, P, Q, equals, left bracket, x, plus, 12, right bracket, degreesm∠RPQ=(x+12) ∘ . Find m, angle, R, P, Q, .m∠RPQ.

Answer 1

In ΔPQR, m∠RPQ = 25°.

In a triangle, the sum of all angles is 180 degrees. Therefore, we have the equation:

m∠PQR + m∠RPQ + m∠QRS = 180°

Substituting the given values:

(3x + 13)° + (x + 12)° + (7x + 7)° = 180°

Combining like terms:

11x + 32 = 180

Subtracting 32 from both sides:

11x = 148

Dividing both sides by 11:

x = 13

Substituting the value of x in the expression for m∠RPQ:

m∠RPQ = (13) + 12 = 25°

Therefore, m∠RPQ = 25°.