Question

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

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((8x + 8)^{\circ}+61^{\circ}+41^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add the constant angles: \(61 + 41=102\). The equation becomes \(8x+8 + 102=180\), which simplifies to \(8x+110 = 180\).

Step3: Solve for \(x\)

Subtract \(110\) from both sides: \(8x=180 - 110\), so \(8x=70\). Then divide both sides by \(8\): \(x=\frac{70}{8}=\frac{35}{4}=8.75\).

Answer:

\(x = 8.75\)