Question

if m ||n and m∠e = 100° in the figure to the right, find the measures of ∠a, ∠c, and ∠h. m∠a = (type an integer or a decimal.)

Explanation:

Step1: Identify corresponding angles

Since \(m\parallel n\), \(\angle a\) and \(\angle e\) are corresponding angles. Corresponding angles formed by parallel - lines and a transversal are congruent. So \(m\angle a=m\angle e = 100^{\circ}\).

Step2: Identify vertical angles

\(\angle c\) and \(\angle a\) are vertical angles. Vertical angles are congruent. So \(m\angle c=m\angle a = 100^{\circ}\).

Step3: Identify alternate - exterior angles

\(\angle h\) and \(\angle e\) are alternate - exterior angles. Alternate - exterior angles formed by parallel lines and a transversal are congruent. So \(m\angle h=m\angle e=100^{\circ}\).

Answer:

\(m\angle a = 100^{\circ}\), \(m\angle c = 100^{\circ}\), \(m\angle h = 100^{\circ}\)