Question

1. angle bac = 35° and angle bca = 20°. what is the measure of angle bad?
2. what is the measure of angle abc?

Explanation:

Step1: Use parallelogram property

In parallelogram \(ABCD\), \(AD \parallel BC\), so \(\angle CAD = \angle BCA = 20^\circ\) (alternate interior angles are equal).

Step2: Calculate \(\angle BAD\)

\(\angle BAD = \angle BAC + \angle CAD\)
\(\angle BAD = 35^\circ + 20^\circ = 55^\circ\)

Step3: Use triangle angle sum for \(\angle ABC\)

In \(\triangle ABC\), sum of angles is \(180^\circ\).
\(\angle ABC = 180^\circ - \angle BAC - \angle BCA\)
\(\angle ABC = 180^\circ - 35^\circ - 20^\circ = 125^\circ\)

Answer:

1. \(55^\circ\)
2. \(125^\circ\)