Question

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

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((4x + 3)+90 + 63=180\).

Step2: Simplify the left - hand side of the equation

First, add the constants: \(4x+3 + 153=180\), which simplifies to \(4x+156 = 180\).

Step3: Isolate the term with \(x\)

Subtract \(156\) from both sides: \(4x=180 - 156\). So, \(4x=24\).

Step4: Solve for \(x\)

Divide both sides by \(4\): \(x=\frac{24}{4}\).

Answer:

\(x = 6\)