## points of sides AB and AC of / ABC, 7. In Fig. 13.28, D and E are the mid- Fig 13.27 is a the such that DE || BC. W

Question

points of sides AB and AC of / ABC,
7. In Fig. 13.28, D and E are the mid-
Fig 13.27
is a
the
such that DE || BC. What is
Fig. 13.28
ed
8. The measure of one angle of a parallelogram is 70″, What are the measures
of the remaining angles?
2
9. Two adjacent angles of a parallelogram are equal. What is the measure of
each angle?
(Hint : Sum of adjacent angles is 180)
w
10. Two adjacent angles of a parallelogram are in the ratio 2 : 3. Find the
measures of all the angles.
(Hint: Sum of adjacent angles is 180°)​

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4 weeks 2021-11-06T08:46:12+00:00 1 Answer 0 views 0

## Answers ( )

In parallelogram ABCD, ∠A and ∠B are adjacent angles supplementary to each other.

Thus, we have:

∠A + ∠B = 180°

Also,

∠A = x° and ∠B = (3x + 20)°

⇒ x° + 3x° + 20° = 180°

⇒ 4x° + 20° = 180°

⇒ 4x° = 160°

⇒ x° = 40°

⇒ x = 40

We know that opposite angles of a parallelogram are congruent.

Thus, we have:

∠C = ∠A = x°

⇒∠C= 40°

∠D = ∠B

⇒ ∠D = 3x° + 20°

= 3(40°) + 20°120°

+ 20°

= 140°

∴∠D=140°