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Answer:

x = 12

m(QS) = 52°

m(PD) = 152°

Step-by-step explanation:

Recall: Angle formed by two secants outside a circle = ½(the difference of the intercepted arcs)

Thus:

m<R = ½[m(PD) - m(QS)]

50° = ½[(12x + 8) - (4x + 4)] => substitution

Solve for x

Multiply both sides by 2

2*50 = (12x + 8) - (4x + 4)

100 = (12x + 8) - (4x + 4)

100 = 12x + 8 - 4x - 4 (distributive property)

Add like terms

100 = 8x + 4

100 - 4 = 8x

96 = 8x

96/8 = x

12 = x

x = 12

✔️m(QS) = 4x + 4 = 4(12) + 4 = 52°

✔️m(PD) = 12x + 8 = 12(12) + 8 = 152°

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