Question

I’m not sure how to solve this. help?

Answer 1

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°