1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Tick (✓) the correct answer: If an angle of a parallelogram is two-thirds of its adjacent angle, the smallest angle of the parallelogram is (a) 54° (b) 72° (c) 81° (d) 108°

Open in App
Solution

## $\left(\mathrm{b}\right)72°\phantom{\rule{0ex}{0ex}}\mathrm{Let}x°\mathrm{be}\mathrm{the}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{parallelogram}.\phantom{\rule{0ex}{0ex}}\mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{adjacent}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{is}180°.\phantom{\rule{0ex}{0ex}}\therefore x+\left(\frac{2}{3}×x\right)=180\phantom{\rule{0ex}{0ex}}⇒x+\frac{2x}{3}=180\phantom{\rule{0ex}{0ex}}⇒\left(x+\frac{2x}{3}\right)=180\phantom{\rule{0ex}{0ex}}⇒\frac{5x}{3}=180\phantom{\rule{0ex}{0ex}}⇒x=\left(180×\frac{3}{5}\right)\phantom{\rule{0ex}{0ex}}⇒x=108\phantom{\rule{0ex}{0ex}}\mathrm{Hence},\mathrm{one}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{parallelogram}\mathrm{is}108°.\phantom{\rule{0ex}{0ex}}\mathrm{Its}\mathrm{adjacent}\mathrm{angle}=\left(180-108\right)°=72°\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},\mathrm{the}\mathrm{smallest}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{parallelogram}\mathrm{is}72°.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

Suggest Corrections
1
Join BYJU'S Learning Program
Related Videos
Diagonals of a Parallelogram divides it into two congruent triangles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program