Answer:
m∠W = 80°
Explanation:
To find m∠W, remember that:
One exterior angle of a triangle is equal to the sum of the other two interior angles.
Now apply this information.
Notice that point U has an exterior angle. It will be equivalent to the sum of m∠V and m∠W, or in algebraic from: U = m∠V + m∠W
Substitute the information we know.
U = m∠V + m∠W
10x + 10 = 30 + 9x - 10 Simplify the right side's like terms.
10x + 10 = 20 + 9x Isolate "x"
10x - 9x + 10 = 20 + 9x - 9x Subtract 9x from both sides
10x - 9x + 10 = 20 9x cancels out on the right side
x + 10 = 20 Simplified left side, 10x - 9x = x
x + 10 - 10 = 20 - 10 Subtract 10 from both sides
x = 20 - 10 "x" is isolated. Simplify right side.
x = 10 Solved for "x"
To find m∠W, substitute the value of "x" into the equation of its angle.
m∠W = 9x - 10
m∠W = 9(10) - 10 Multiply 9 and 10, then subtract 10 from the product.
m∠W = 80
Write with the units, degrees symbol °
Therefore the measure of ∠W is 80°.