In a quadrilateral ABCD , AB || DC . If angle A : angle D = 2:3 and angle B : angle C = 7:8 , find the measure of each angle

Guest Sep 19, 2020

#1**+1 **

In a quadrilateral ABCD , AB || DC . If angle A : angle D = 2:3 and angle B : angle C = 7:8 , find the measure of each angle

**Hello Guest!**

\(\alpha :(180^{\circ} -\alpha )=2:3\\ 3\alpha =360^{\circ} -2\alpha\\ 5\alpha=360^{\circ} \)

\(\alpha =72^{\circ}\)

\(\beta:(180^{\circ} -\beta)=7:8\\ 8\beta=1440^{\circ} -7\beta\\ 15\beta=1440^{\circ} \)

\(\beta=96^{\circ} \)

\(\gamma=180^{\circ} -\beta=180^{\circ} -96^{\circ} \)

\(\gamma=84^{\circ} \)

\(\delta=180^{\circ} -\alpha=180^{\circ} -72^{\circ} \)

\(\delta=108^{\circ} \)

!

asinus Sep 19, 2020