Question

if mn =qp and on producing mn and qp intersect at r also mq parallel np if angle nmq is 65 then angle r is​

Answer 1

Hope it would be able to help yourself

Answer 2

Angle R would be 50°

Step-by-step explanation:

Given,

mn = qp

⇒ m∠NMQ = m∠PQM

But, m∠NMQ = 65°

⇒ m∠PQM = 65°

Note : The adjacent interior angle subtended by non parallel sides in isosceles trepezoid are equal in measure,

Now, MQ ║ NP

By Alternate interior angle theorem,

m∠NMQ = m∠RNP and m∠PQM = m∠RPN

⇒ m∠RNP = m∠RPN = 65°,

In triangle RNP,

m∠RNP + m∠RPN + m∠NRP = 180°

65° +  65° + m∠NRP = 180°

130° + m∠NRP = 180°

⇒ m∠NRP = 180° - 130° = 50°

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