Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y Z and Y Z X are congruent. Consider isosceles ΔXYZ. What is the value of n? What is the measure of leg XY? ft What is the measure of leg XZ? ft

The value of n is 3, the measure of leg XY is 39 ft, and the measure of XZ is 39 ft and this can be determined by using the properties of an isosceles triangle.

Given :

Given that the angle XYZ and angle YZX are congruent to each other and triangle XYZ is an isosceles triangle.

From the above statement, it can be concluded that the side length of XY and the side length of XZ is also congruent to each other, that is:

XY = XZ

9n + 12 = 15n - 6

Simplify the above expression in order to determine the value of 'n'.

18 = 6n

n = 3 ft

The measure of leg XY is given by:

XY = 9(3) + 12 = 39 ft

The measure of leg XZ is given by:

XZ = 15(3) - 6 = 39 ft

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Step-by-step explanation:

Given

Solving (a): n

To solve for n;

We make use of

Substitute values for XY and XZ

Divide through by -6

Solving (b) XY

Substitute 3 for n

Solving (c): XZ

a. 32 degrees

step-by-step explanation:

here we have to use the rule.

m∠e = 1/2 (major arc - minor arc)

m∠e = 1/2 (212 - 148)

m∠e = 1/2 (64)

m∠e = 32 degrees

answer: a. 32 degrees

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