Question

ABCD is a parallelogram in which a pair of adjacent are in the ratio 1:2. Find the measure of all the angles

Answer 1

$\mathfrak{\underline{Answer:-\angle A = 60,\:\angle B = 120, \angle C = 60, \:\angle D = 120 }}$

$\rule{100}2$

$\textbf{\underline{\underline{Step-By-Step\:Explanation:-}}}$

In ║gm ABCD,

Ratio of adjacent angles = 1 : 2,

Let the common factor in both the angles be ' P ' .

So,

Adjacent angles of ║gm ABCD will become 1P and 2P

Also, we know that the sum of adjacent angles of ║gm makes a sum of 180°

So,

$\sf P + 2P$ = 180°

⇒ 3P = 180°

$\implies \sf P =\dfrac{180}{3}$

∴ P = 60°

Now,

Let ∠A and ∠B are adjacent angles.

So, ∠A = 60°, ∠B = 2 × 60 = 120°;

We know that, opposite angles of ║gm are equal. So, ∠C = ∠A = 60° and ∠D = ∠B = 120°

$\rule{100}2$

$\star\mathscr\orange{Verification:-}$

In a ║, all the interior angles makes a sum of 360°

= 60° + 60° + 120° + 120°

= 120° + 240°

= 360°

Hence Proved!

$\rule{200}2$