Question

the measures of the angles of a triangle are shown in the figure below. solve for x.

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°.
So, \(90^{\circ}+30^{\circ}+(2x + 16)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side

First, add the known angles: \(90 + 30=120\).
The equation becomes \(120+(2x + 16)=180\).
Combining like terms, we get \(2x+136 = 180\).

Step3: Solve for x

Subtract 136 from both sides: \(2x=180 - 136\).
\(2x = 44\).
Divide both sides by 2: \(x=\frac{44}{2}\).

Answer:

\(x = 22\)