Question

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

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). One angle is \(90^\circ\) (right angle), another is \(23^\circ\), and the third is \((8x + 3)^\circ\). So, \(90 + 23 + (8x + 3) = 180\).

Step2: Simplify the equation

Combine like terms: \(90 + 23 + 3 + 8x = 180\) → \(116 + 8x = 180\).

Step3: Solve for x

Subtract 116 from both sides: \(8x = 180 - 116 = 64\). Then divide by 8: \(x = \frac{64}{8} = 8\).

Answer:

\(x = 8\)