Question

The figure below shows the design of a truss to support the weight of a roof. In this truss design, ∠A⩭∠D and ĀF⩭DF.

Answer 1

Answer:

$m\angle A= 30^{\circ}$

Step-by-step explanation:

In the question, we're given $\angle A\cong \angle D$. Therefore, the measure of these two angles must be equal.

To find the value of $x$, set these two angles equal to each other:

$4x-26=x+16$

Add 26 and subtract $x$ from both sides:

$3x=42$

Divide both sides by 3:

$x=\frac{42}{3}=14$

Since $\angle A$ was labelled as $4x-26$, substitute $x=14$ to find its measure:

$\angle A=4(14)-26,\\\angle A=56-26,\\\angle A=\boxed{30^{\circ}}$

You can also substitute $x=14$ into the label of angle D as angle A is congruent to angle D for easier calculations ($14+16=\boxed{30^{\circ}}$).