Question

towers a lookout tower sits on a network of struts and posts. leslie measured two angles on the tower: ( mangle 1 = (7x - 7)^circ ), ( mangle 2 = (4x + 2)^circ ), and ( mangle 3 = (2x + 6)^circ ), what is ( mangle 1 )?

Explanation:

Step1: Identify angle relationship

Assuming the angles form a straight line (supplementary or triangle sum, but likely straight line as tower struts form linear pair or triangle? Wait, maybe triangle? Wait, no, the diagram shows a tower with struts, so maybe the three angles are in a triangle? Wait, no, the problem says "two angles" but gives three? Wait, maybe typo, but likely the three angles are related, maybe ∠1 is an exterior angle, so ∠1 = ∠2 + ∠3 (exterior angle theorem). So set \( 7x - 7 = (4x + 2) + (2x + 6) \)

Step2: Solve for x

Simplify right side: \( 4x + 2 + 2x + 6 = 6x + 8 \)
Equation: \( 7x - 7 = 6x + 8 \)
Subtract \( 6x \) from both sides: \( x - 7 = 8 \)
Add 7 to both sides: \( x = 15 \)

Step3: Find m∠1

Substitute x = 15 into \( 7x - 7 \): \( 7(15) - 7 = 105 - 7 = 98 \)

Answer:

\( 98^\circ \)