Question

ab and ec are perpendicular. find the value of x and m < heb if the measure of m∠heb = 2x and the m < ceh = x + 6.

Explanation:

Step1: Use perpendicular - angle property

Since \(AB\) and \(EC\) are perpendicular, \(\angle CEB = 90^{\circ}\), and \(\angle CEH+\angle HEB=\angle CEB\). So \(x + 6+2x=90\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(3x+6 = 90\). Subtract 6 from both sides: \(3x=90 - 6=84\). Divide both sides by 3: \(x=\frac{84}{3}=28\).

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

Substitute \(x = 28\) into the expression for \(\angle HEB\). Since \(m\angle HEB = 2x\), then \(m\angle HEB=2\times28 = 56^{\circ}\).

Answer:

\(x = 28\)
\(m\angle HEB=56^{\circ}\)