Question

Q17. The top of a table is in the form of a parallelogram such that the ratio
of its one of the interior angles and exterior angle is 1:3. Then find the
measure of all the angles​

Answer 1

ANSWER:

Given:

• Ratio of one of the interior angles to its corresponding exterior angle is 1:3.

To Find:

• Measure of all angles of the parallelogram.

Assumption:

• Let the interior angle(ABC) be x.
• Hence, the corresponding exterior angle(ABE) is 3x.

Solution:

(Refer the attachment for labelling)

We know that, the interior angle and its corresponding exterior angle are angles in  linear pair, i.e., they both add upto 180°.

So,

⇒ x + 3x = 180°

⇒ 4x = 180°

⇒ x = 180/4 = 45°.

⇒ Angle ABC = 45°

We know that,

⇒ Angle ABC + Angle BCD = 180° (adjacent angles are supplementary)

⇒ 45° + Angle BCD = 180°

⇒ Angle BCD = 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:

• Interior angle and its corresponding exterior angle are angles in linear pair.
• Adjacent angles are supplementary.
• Opposite angles of a parallelogram are equal.

Important Points:

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