Question

The consecutive angles of a parallelogram are in the ratio 2:3. The smallest angle is

Answer 1

Step-by-step explanation:

Two consecutive angles of this parallelogram are 72° and 108°

Step-by-step explanation:

The sum of two consecutive angles of a parallelogram is 180°

Consider the two consecutive angle of a parallelogram are ∠A and ∠B

Therefore,

∠A+∠B=180° ...................... equation-1

The ratio between two angles are 2:3

So, consider the ∠A= 2x and ∠B=3x

Putting the value of ∠A and ∠B in equation-1 we get,

\begin{gathered}2x+3x=180\\\\\Rightarrow5x=180\\\\\Rightarrow{x}=\frac{180}{5}=36\end{gathered}

2x+3x=180

⇒5x=180

⇒x=

5

180

=36

So the angles are ∠A=72 and ∠B=108

Two consecutive angles of this parallelogram are 72° and 108°