Question

find the measure of angle a. 5)

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, $(7x - 2)+(5x + 3)+83=180$.

Step2: Combine like - terms

First, simplify the left - hand side of the equation: $(7x+5x)+(-2 + 3)+83=180$, which gives $12x+1 + 83=180$, then $12x+84=180$.

Step3: Isolate the variable term

Subtract 84 from both sides of the equation: $12x=180 - 84$, so $12x=96$.

Step4: Solve for x

Divide both sides by 12: $x=\frac{96}{12}=8$.

Step5: Find the measure of angle A

Substitute $x = 8$ into the expression for angle A: $7x-2=7\times8 - 2=56 - 2=54$.

Answer:

$54^{\circ}$