Question

find x if m∠rqp = 8x - 4, m∠rqe = 34 deg, and m∠eqp = 4x + 6.
options: -6, 11, 9, 1

Explanation:

Step1: Set up angle addition equation

$m\angle RQP = m\angle RQE + m\angle EQP$

Step2: Substitute given expressions

$8x - 4 = 34 + 4x + 6$

Step3: Simplify right-hand side

$8x - 4 = 4x + 40$

Step4: Isolate x terms

$8x - 4x = 40 + 4$

Step5: Solve for x

$4x = 44 \implies x = \frac{44}{4} = 11$

Answer:

11