Question

in below diagram, line ab is parallel to cd, i.e. ab || cd. ∠egb = 57. ∠egb and ∠ehd are congruent because they are corresponding. so the m∠ehd = 57 degrees.

Explanation:

Step1: Identify angle - relationship

Since \(AB\parallel CD\), \(\angle EGB\) and \(\angle EHD\) are same - side interior angles.

Step2: Recall property of same - side interior angles

Same - side interior angles of parallel lines are supplementary, i.e., their sum is \(180^{\circ}\). Given \(\angle EGB = 57^{\circ}\).
Let \(m\angle EHD=x\). Then \(m\angle EGB + m\angle EHD=180^{\circ}\), so \(57^{\circ}+x = 180^{\circ}\).

Step3: Solve for \(m\angle EHD\)

\(x=180^{\circ}- 57^{\circ}=123^{\circ}\).

Answer:

\(123\)