Question

a lookout tower sits on a network of struts and posts. leslie measured three angles on the tower. if ( mangle1 = (7x - 7)^circ ), ( mangle2 = (4x + 2)^circ ), and ( mangle3 = (2x + 6)^circ ), what is ( mangle1 )?

Explanation:

Step1: Recognize angle relationship

From the tower structure, $\angle 1$ is an exterior angle of the triangle formed by $\angle 2$ and $\angle 3$, so $m\angle 1 = m\angle 2 + m\angle 3$.

Step2: Substitute angle expressions

$$(7x - 7) = (4x + 2) + (2x + 6)$$

Step3: Simplify right-hand side

$$7x - 7 = 6x + 8$$

Step4: Solve for $x$

$$7x - 6x = 8 + 7$$
$$x = 15$$

Step5: Calculate $m\angle 1$

Substitute $x=15$ into $m\angle 1=(7x-7)^\circ$:
$$m\angle 1 = 7\times15 - 7 = 105 - 7$$

Answer:

$98^\circ$