Question

the measures of the angles of a triangle are shown in the figure below. solve for x.
answer attempt 1 out of 2
x

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). This triangle is right - angled, so one angle is \(90^\circ\), another is \(42^\circ\), and the third is \((4x + 16)^\circ\). So we can write the equation: \(90+42+(4x + 16)=180\).

Step2: Simplify the left - hand side

First, add the constant terms: \(90+42 + 16=148\). So the equation becomes \(148+4x=180\).

Step3: Solve for x

Subtract 148 from both sides: \(4x=180 - 148\). Calculate \(180-148 = 32\), so \(4x = 32\). Then divide both sides by 4: \(x=\frac{32}{4}=8\).

Answer:

\(x = 8\)