Question

3 parallelogram abcd
13 cm
a
d
3 cm
17
ab=
cm
m∠a=

m∠c=

Explanation:

Step1: Use the property of parallelogram (opposite sides are equal)

In parallelogram \(ABCD\), \(AB = CD\). Given \(CD = 3\mathrm{cm}\), so \(AB=3\mathrm{cm}\).

Step2: Use the property of adjacent angles in parallelogram (supplementary)

In parallelogram \(ABCD\), \(\angle A+\angle B = 180^{\circ}\). Given \(\angle B=17^{\circ}\), then \(\angle A=180^{\circ}-\angle B\).
\(\angle A = 180 - 17=163^{\circ}\)

Step3: Use the property of opposite angles in parallelogram (equal)

In parallelogram \(ABCD\), \(\angle C=\angle A\). Since \(\angle A = 163^{\circ}\), so \(\angle C=163^{\circ}\)

Answer:

\(AB = 3\mathrm{cm}\), \(m\angle A=163^{\circ}\), \(m\angle C = 163^{\circ}\)