Question

In Fig. 5.11, if AB || CD, ∠ APQ = 50o

and ∠PRD = 130o

, then find ∠ QPR .​

Answer 1

Answer:

We know that, ∠APR = ∠PRD … [because interior alternate angles] ∠APQ + ∠QPR = 130o 50o + ∠QPR = 130o ∠QPR = 130o – 50o ∠QPR = 80 if-ab-cd-apq-50-and-prd-130-then-qpr-is-a-130-b-50-c-80-d-30

answer is 80

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Answer 2

Given:

• AB || CD
• ∠APQ = 50°
• ∠PRD = 130°

To Find:

• ∠QPR = ?

Solution:

If AB || CD and PR is a transversal, we get:

∠APR = ∠PRD [Alternate Interior Angles]

As, ∠APR = ∠APQ + ∠QPR, we get:

∠APQ + ∠QPR = ∠PRD

Providing given values to the angles, we get:

50° + ∠QPR = 130°

Evaluating further, we get:

∠QPR = 130° - 50°

∠QPR = 80°

Hence, ∠QPR = 80°

Extra Information:

• Two lines (take a and b) are said to be parallel if the distance between the two lines are always same, however far they are extended.
• Transversal is a line which intersects two or more lines at a point.

In the image attached:

• Corresponding Angles are (∠1, ∠5), (∠2, ∠6), (∠3, ∠7), (∠4, ∠8). Corresponding Angles are always equal.
• Alternate Interior Angles are (∠3, ∠5), (∠4, ∠6). Alternate Interior Angles are always equal.
• Alternate Exterior Angles are (∠2, ∠8), (∠2, ∠8). Alternate Exterior Angles are always equal.
• Consecutive Interior Angles are (∠3, ∠6), (∠4, ∠5). They are also called co-interior angles. Sum of Consecutive Interior Angles are always 180°.