Question

c#7 the angles ∠ghi and ∠jhk are vertical to each other. knowing that m∠ghi=(5x + 13)° and m∠jhk=(7x - 21)°: sketch a picture of the situation, solve for x, and find m∠ghi. x = ______ m∠ghi = ______

Explanation:

Step1: Set up the equation

Since vertical angles are equal, \(5x + 13=7x - 21\).

Step2: Solve for \(x\)

Subtract \(5x\) from both sides: \(13 = 2x-21\).
Add \(21\) to both sides: \(34 = 2x\).
Divide both sides by \(2\): \(x = 17\).

Step3: Find \(m\angle GHI\)

Substitute \(x = 17\) into \(m\angle GHI=(5x + 13)^{\circ}\).
\(m\angle GHI=(5\times17 + 13)^{\circ}=(85 + 13)^{\circ}=98^{\circ}\).

Answer:

\(x = 17\), \(m\angle GHI=98^{\circ}\)