Question

Find the value of x. Please show the work and explain! thank you

Answer 1

Answer:

64°

Step-by-step explanation:

Let's answer the guiding questions:

"1. What kind of triangle is this?"

Since two of the triangle's legs are the same length, this is an isosceles triangle.

"2. What does that tell me about the angles?  Which two angles are congruent?"

Isosceles triangles have a vertex angle (the angle between the congruent sides) and two base angles.  The base angles are congruent.

"3. How can we use congruent angles and the triangle sum theorem to solve for x?"

Since we know the third angle is 58°, and that angles of a triangle add up to 180°, we can write and solve an equation.

x + 58° + 58° = 180°

x + 116° = 180°

x = 64°