Question

1. find x if m∠abe = x + 87, m∠abc = 162°, and m∠ebc = x + 89.

Explanation:

Step1: Use angle - addition postulate

We know that \(m\angle ABC=m\angle ABE + m\angle EBC\). So, \((x + 87)+(x + 89)=162\).

Step2: Combine like - terms

Combining the \(x\) terms and the constant terms on the left - hand side gives \(2x+176 = 162\).

Step3: Isolate the variable term

Subtract 176 from both sides: \(2x=162 - 176\), so \(2x=-14\).

Step4: Solve for \(x\)

Divide both sides by 2: \(x=\frac{-14}{2}=-7\).

Answer:

\(x = - 7\)