Question

If an angle of a parallelogram is two-third of

Answer 1

Answer:

We know that in a parallelogram two opposite angles are equal -

$\\ \implies \sf \: 2x + 2y = 360 {}^{ \circ} \\ \\ \\ \implies \sf \: x + y = 180 {}^{ \circ} \qquad \quad \: (i)$

Given -

• angle x is equal to the two - third of it's adjacent angle y.

$\\ \implies \sf \: x = \frac{2}{3} y \\ \\ \\ \implies \sf \frac{x}{2} = \frac{y}{3} = k \\ \\ \\ \qquad \sf \small \underline{ x = 2k \: \: \& \: \: y = 3k}$

Now, by using equation (1) :

$\\ \implies \sf \: 2k + 3k = 180 \\ \\ \\ \implies \sf \: 5k = 180 \\ \\ \\ \implies \sf \: k = \frac{180}{5} \\ \\ \\ \large{ \boxed{ \sf{k = {36}^{ \circ} }}}$

Now, by putting the value of k in x and y.

• x = 2k = 2 × 36 = 72°
• y = 3k = 3 × 36 = 108°

Therefore, the right option and smallest angle is b) 72°.