Question

If one angle of a parallelogram is 60 degree, find the other angles

Answer 1

In the figure :

ABCD is a parallelogram.

∠DAB = 60°

In a parallelogram , opposite angles are equal .

∴∠DAB =∠DCB =60°


Also , in a parallelogram , adjacent angles are supplementary.

∠DAB + ∠ABC = 180°
∠ABC = 180° - 60°
= 120°

∠ABC = ∠ADC =120° [opposite angles are equal]

Answer 2

Given is an angle of a parallelogram, Find its other angles.

Explanation:

• Let the parallelogram be denoted by PQRS and its angles be denoted by P, Q, R, and S respectively.
• Here the pair of angles P, R and angles Q, S form the pair of the opposite angles and are equal in measure, $\angle P=\angle R,\ \angle Q= \angle S$   ---(a)
• Here the pair of angles P, Q and angles R, S form the pair of adjacent angles and have a sum of $180$°,
•                            $\angle P +\angle Q=\angle R+\angle S=180$°    ---(b)
• Let the given measure of angle be of P, $\angle P = 60$  
• Then from (a) we get, $\angle R=60$
• Now from (b) we get,  
•                                  $\angle Q=\angle S= 180-60\\->\angle Q=\angle S= 120$  
• Hence, the measurements of other angles of the parallelogram are $120, 60, 120$ degrees respectively.