Question

Find the unknown angles of

Answer 1

x=70

y=70

z=110

Explanation:

This is an isosceles triangle because of the two equal sides. This means that x and y are congruent. We know that the angles in a triangle add up to 180°, so x+y+40=180. We also know that x=y so put in x for y in the equation.

x+x+40=180

2x=180-40

2x=140

x=70, since x=y so y=70

Supplementary angles(angles on a straight line) add up to 180°.

So y+z=180

We can replace y with 70

70+z=180

z=180-70

z=110

Answer 2

x = y = 70° , z = 110°

Explanation:

Since the legs of the triangle are congruent (equal), indicated by the dashes through the 2 equal sides.

Then the triangle is isosceles with congruent base angles , so x = y

the sum of the 3 angles in the triangle = 180° , that is

x + y + 40° = 180° ( since x = y )

x + x + 40° = 180° ( subtract 40° from both sides )

2x = 140° ( divide both sides by 2 )

x = 70°

and since y = x , then y = 70°

y and z lie on a straight line and are a linear pair , which sum to 180° , so

y + z = 180° , that is

70° + z = 180° ( subtract 70° from both sides )

z = 110°

x = y = 70° and z = 110°