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°.

Step2: Set up the equation

We have a right - triangle with angles 90°, 36°, and (7x - 2)°. So, 90+36+(7x - 2)=180.

Step3: Simplify the left - hand side

First, combine like terms: (90 + 36-2)+7x=180, which gives 124 + 7x=180.

Step4: Solve for x

Subtract 124 from both sides: 7x=180 - 124, so 7x=56. Then divide both sides by 7: x = 8.

Answer:

8