Question

find the measure of angle a. 21) triangle with angles: 84°, x + 59, and angle a labeled x + 51

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x + 59)+84+(x + 51)=180\).
Simplify the left - hand side: \(x+x+59 + 84+51=180\), \(2x+194 = 180\).

Step2: Solve for \(x\)

Subtract \(194\) from both sides: \(2x=180 - 194=-14\).
Divide both sides by \(2\): \(x=-7\).

Step3: Find the measure of angle \(A\)

Angle \(A=x + 51\). Substitute \(x=-7\) into the expression: \(A=-7+51\).

Answer:

\(44^{\circ}\)