pq bisects ∠spy. m∠spq = x-5 and m∠ypq= 4x- solve for x and find m∠spy

X = 5/3 and m∠SPY = 8 1/3°.

Since PQ bisects the angle, the two angles formed by the bisector are equal:

11/2x - 5 = 4x - 5/2

We will first multiply everything by 2 to eliminate the fractions:
(11/2x)*2 - 5*2 = 4x*2 - (5/2)*2
11x - 10 = 8x - 5

Subtract 8x from each side:
11x - 10 - 8x = 8x - 5 - 8x
3x - 10 = -5

Add 10 to both sides:
3x - 10 + 10 = -5 + 10
3x = 5

Divide both sides by 3:
3x/3 = 5/3
x = 5/3

Now we will plug this in for x in both smaller angles and add them together to find the measure of ∠SPY:

11/2(5/3) - 5 + 4(5/3) - 5/2
55/6 - 5 + 20/3 - 5/2

We will rewrite everything using a denominator of 6:
55/6 - 30/6 + 40/6 - 15/6 = (55-30+40-15)/6 = 50/6 = 8 2/6 = 8 1/3°