Final answer:
By setting the expressions for angles X and Y equal to each other in the isosceles triangle WXY, we find that x = 18, which allows us to calculate each angle's measure: W = 24°, X = 78°, and Y = 78°.
Step-by-step explanation:
In triangle WXY, we are given that WX is congruent to WY, which means that angles X and Y are also congruent because of the Isosceles Triangle Theorem. As a result, we can set the expressions for X and Y equal to each other to find the value of x:
X = Y
5x - 12 = 7x - 48
Solving this equation for x, we get:
2x = 36
x = 18
Since we now have x, we can determine the measure of each angle:
W = x + 6 = 18 + 6 = 24°
X = 5x - 12 = 5(18) - 12 = 78°
Y = 7x - 48 = 7(18) - 48 = 78°
The measures of angles W, X, and Y are 24°, 78°, and 78°, respectively.
Learn more about Angle Measures in Isosceles Triangle