If arc QR=3x+38 degrees , arc PS=5x-10 degrees ,and

Arc QR = 111.5°

Step-by-step explanation:

Given:

Arc QR = (3x + 38)°

Arc PS = (5x - 10)°

m<QMP = 68°

Required:

Measure of arc QR

Solution:

Recall: Angles of intersecting chords theorem states that the angle formed equals half of the sum of the intercepted arcs

This by implication means:

m<1 = ½(arc QR + arc PS)

We are given arc QR, and arc PS.

m<1 = 180° - m<QMP (angles on a straight line)

m<1 = 180° - 68°

m<1 = 112°

Plug in the values into the equation and solve for x

112° = ½(3x + 38 + 5x - 10)

Multiply both sides by 2

2*112 = 3x + 38 + 5x - 10

224 = 3x + 38 + 5x - 10

Add like terms

224 = 8x + 28

224 - 28 = 8x + 28 - 28

196 = 8x

196/8 = 8x/8

24.5 = x

x = 24.5

✅Let's find arc QR

Arc QR = (3x + 38)°

Plug in the value of x

Arc QR = 3(24.5) + 38 = 73.5 + 38

Arc QR = 111.5°

its a little blurry tbh

step-by-step explanation:

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step-by-step explanation: