Question

1
Solve for x in the triangle below. Show your work!
2
84
Xº
Y
N

Answer 1

x = 48°

Explanation:

In the given triangle XYZ,

Sides XY and XZ are congruent.

Therefore, both the sides will be equal in measure.

By the definition of isosceles triangle,

"Opposite angles of the equal sides are equal in measure"

m∠Y = m∠Z = x°

m∠X = 84° [Given]

By the triangle sum theorem,

m∠X + m∠Y + m∠Z = 180°

84° + x° + x° = 180°

2x = 180 - 84

x = 48°

Therefore, measure of x = 48° will be the answer.