Question

Please explain how to get X

Answer 1

x = 30°

Explanation:

the first triangle is equilateral.

An equilateral triangle has also congruent angles whose measure is 60°

The vertex of the under triangle is the supplementary of the angle of the equilateral triangle

180 - 60 = 120°

the triangle is isosceles because the two oblique sides are congruent

An isosceles triangle has two congruent base angles

120 + 2x = 180

2x = 180 - 120

2x = 60

2 / 2 x = 60/2

x = 30°

Answer 2

x = 30

y = 5

Explanation:

The triangle to the left has all congruent angles.

Since the sum of the measures of the angles of a triangle is 180°, and all angles are congruent, then each angle measures 180°/3 = 60°.

An equiangular triangle (all angles are congruent) is also an equilateral triangle (all sides are congruent.

Since one side of the left triangle measures 40, then all sides of the left triangle measure 40.

Now let's look at the triangle on the right side. One side measures 40. The left side also measures 40 since we know from the triangle at left. Opposite angles of congruent sides are congruent. The bottom right angle of the triangle to the right also measures x°. The upper angle is the supplement of 60°, so it measures 120°.

x + x + 120 = 180

2x = 60

x = 30

The upper left small triangle is equilateral.

8y = 40

y = 5