Question

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

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is $180^\circ$. So, $42^\circ + 78^\circ + (4x)^\circ = 180^\circ$.

Step2: Simplify the left side

Add $42$ and $78$: $42 + 78 = 120$. So the equation becomes $120 + 4x = 180$.

Step3: Solve for x

Subtract $120$ from both sides: $4x = 180 - 120 = 60$. Then divide by $4$: $x = \frac{60}{4} = 15$.

Answer:

$x = 15$