Question

as shown in the figure, in parallelogram $abcd$, $m$ is a point on the extension of $overline{bc}$. if $mangle mcd = 40^{circ}$, then the measure of $angle a$ is ___. a $140^{circ}$ b $145^{circ}$ c $165^{circ}$ d $155^{circ}$

Explanation:

Step1: Use adjacent - angle property

In parallelogram \(ABCD\), \(AB\parallel CD\). \(\angle BCD\) and \(\angle MCD\) form a linear - pair. Since \(\angle MCD = 40^{\circ}\), then \(\angle BCD=180^{\circ}-\angle MCD\).
\(\angle BCD = 180 - 40=140^{\circ}\)

Step2: Use opposite - angle property

In a parallelogram, opposite angles are equal. \(\angle A\) and \(\angle BCD\) are opposite angles. So \(\angle A=\angle BCD\).
\(\angle A = 140^{\circ}\)

Answer:

A. \(140^{\circ}\)