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

`m\angle A= 30^(\circ)`

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=(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)}`).