Question

Exercise 3.3
A) The adjacent angles of a parallelogram are in the ratio 1: 3. Then find all
the interior angles of a parallelogram.​

Answer 1

ANSWER:

Given:

• Ratio of one angles to its corresponding adjacent angle is 1:3.

To Find:

• Measure of all interior angles of the parallelogram.

Assumption:

• Let the angle(ABC) be x.
• Hence, the corresponding adjacent angle(BCD) is 3x.

Solution:

(Refer the attachment for labelling)

We know that, the angle and its corresponding adjacent angle are supplementary ,i.e., they both add upto 180°.

So,

⇒ x + 3x = 180°

⇒ 4x = 180°

⇒ x = 180/4 = 45°.

⇒ Angle ABC = 45°

⇒ Angle BCD = 3x = 45*3 = 135°

We know that, opposite angles of a parallelogram are equal.

So, the angles are:

⇒ Angle ABC = Angle ADC = 45°

⇒ Angle BCD = Angle BAD = 135°

Concept used:

• Adjacent angles are supplementary.
• Opposite angles of a parallelogram are equal.

Important Points:

• Supplementary = Adding to 180°
• Adjacent angles = Angles which share 1 common arm.
• Opposite angles = Angles which do not share any common arm.