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In triangle WXY, if WX is congruent to WY, then w=(x+6), X=(5x-12), and y=(7x-48), find x and the measure of each angle?

User Gabaros
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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

User James Cazzetta
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