Answer:
The measure of ∠GKH is 27°
Step-by-step explanation:
- In the isosceles triangle, the base angles are equal in measures
- The measure of an exterior angle at a vertex of a triangle equals the sum of the measures of two opposite interior angles
In Δ HJK
∵ HJ = JK
→ That means the triangle is isosceles
∴ Δ HJK is an isosceles triangle
∵ ∠JHK and ∠JKH are base angles
→ By using the first rule above
∴ m∠JHK = m∠JKH
∵ m∠HJK = 70°
∵ m∠JHK + m∠JKH + m∠HJK = 180° ⇒ interior angles of a triangle
∴ m∠JHK + m∠JKH + 70 =180
→ Subtract 70 from both sides
∴ m∠JHK + m∠JKH = 110
→ Divide their sum by 2 to find the measure of each one
∴ m∠JHK = m∠JKH = 110 ÷ 2 = 55°
∵ ∠JHK is an exterior angle of ΔGHK at vertex H
∵ ∠HGK and ∠GKH are the opposite interior angles to ∠JHK
→ By using the 2nd rule above
∴ m∠JHK = m∠HGK + m∠GKH
∵ m∠JHK = 55°
∵ m∠HGK = 28°
∴ 55 = 28 + m∠GKH
→ Subtract 28 from both sides
∴ 27° = m∠GKH
∴ The measure of ∠GKH is 27°
