Question

1. the figure below shows the design of a truss to support the weight of a roof. in this truss design, \\(\angle a \cong \angle d\\) and \\(\overline{af} \cong \overline{df}\\). if \\(m\angle a = 4x - 32\\) and \\(m\angle d = x + 16\\), calculate \\(m\angle a\\). \\(m\angle a = \underline{\quad\quad}\\).

Explanation:

Step1: Set angles equal (congruent)

$4x - 32 = x + 16$

Step2: Isolate x variable

$4x - x = 16 + 32$
$3x = 48$
$x = \frac{48}{3} = 16$

Step3: Substitute x into ∠A formula

$m\angle A = 4(16) - 32$

Answer:

$16^\circ$