Quadrilateral EFGH is an isosceles trapezoid and m∠E=3z+93°. What is the value of z?

z = 4°

Solution:

Given EFGH is an isosceles trapezoid.

By the property of isosceles trapezoid, non-parallel sides are congruent.

⇒ GH = EF

Angles opposite to equal sides are congruent.

∠H ≅ ∠G

m∠H = m∠G

105° = 3z + 93°

Subtract 93° from both sides, we get

12° = 3z

Divide by 3 on both sides, we get

4° = z

Switch the sides.

z = 4°

Hence the value of x is 4°.