Question

find the measure of angle
21)

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x + 59)+84+(x + 51)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x+x)+(59 + 51+84)=180\), which is \(2x+(110 + 84)=180\), and further \(2x+194 = 180\).

Step3: Solve for \(x\)

Subtract \(194\) from both sides: \(2x=180 - 194=-14\). Then divide both sides by \(2\): \(x=\frac{-14}{2}=-7\).

Step4: Find the measure of angle \(A\)

Substitute \(x=-7\) into \(x + 51\). So, \(\angle A=-7+51 = 44^{\circ}\).

Answer:

\(44^{\circ}\)