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
quadrilateral BCED called?
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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Piper 4 weeks 2021-11-06T08:46:12+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-11-06T08:48:04+00:00

    Answer:

    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°

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