Question

1. point k is in the interior of ∠ghi. if m∠ghk=3x−5 and m∠khi=2x+10, and m∠ghi=120°, find the measure of ∠ghk. a) 23° b) 56° c) 64° d) 120

Explanation:

Step1: Set up the angle addition equation

Since point \( K \) is in the interior of \( \angle GHI \), we know that \( m\angle GHK + m\angle KHI = m\angle GHI \). Substituting the given expressions, we get:
\( (3x - 5) + (2x + 10) = 120 \)

Step2: Solve for \( x \)

Combine like terms:
\( 3x + 2x - 5 + 10 = 120 \)
\( 5x + 5 = 120 \)
Subtract 5 from both sides:
\( 5x = 120 - 5 \)
\( 5x = 115 \)
Divide both sides by 5:
\( x = \frac{115}{5} = 23 \)

Step3: Find \( m\angle GHK \)

Substitute \( x = 23 \) into \( m\angle GHK = 3x - 5 \):
\( m\angle GHK = 3(23) - 5 \)
\( m\angle GHK = 69 - 5 \)
\( m\angle GHK = 64^\circ \)

Answer:

C) \( 64^\circ \)