If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
The congruent angles of a kite are formed by the noncongruent adjacent sides. In our case, the noncongruent adjacent sides are EF and FG, and EH and HG. They form angles ∠ F and ∠ H, respectively. Therefore, ∠ F and ∠ H are congruent.
∠ H≅ ∠ F ⇒ m∠ H= m∠ F
Since ∠ F is a right angle, it measures 90^(∘). This allows us to conclude that ∠ H also measures 90^(∘).
m∠ H= 90^(∘)
By the Corollary to the Polygon Interior Angles Theorem the sum of the measures of the interior angles of any quadrilateral is 360^(∘). Applying it to HEFG, we can form the following equation.
m∠ H+ m∠ E+ m∠ F+m∠ G=360^(∘)
Substituting 90^(∘) for m∠ H and m∠ F, and 110^(∘) for m∠ E, we will get an equation where the only unknown is m∠ G. Let's solve it!
