Question

the measures of the angles of a triangle are shown in the figure below. solve for x. 60° (7x - 12)°

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. So, 60°+90°+(7x - 12)°=180°.

Step2: Simplify the left - hand side

First, add the non - variable angles: 60 + 90=150. The equation becomes 150+(7x - 12)=180. Then, simplify further: 150+7x-12 = 180, which is 7x + 138=180.

Step3: Isolate the variable term

Subtract 138 from both sides of the equation: 7x+138 - 138=180 - 138. So, 7x=42.

Step4: Solve for x

Divide both sides by 7: $\frac{7x}{7}=\frac{42}{7}$. Thus, x = 6.

Answer:

x = 6