Question

in figure MN=QP and producing MN and QP intersect at R. MQ||NP then angle r is​

Answer 1

Answer:

50

Step-by-step explanation:

angle N=65(by parallel lines)

angle M=65(by cyclic quadrilateralMQPN)

R+M+N=180

N=50

Answer 2

$\angle R=50^{\circ}$

Step-by-step explanation:

In triangle RMQ

NP is parallel to MQ

MN=QP

By triangle proportionality theorem

$\frac{RN}{NM}=\frac{RP}{PQ}$

$\frac{RN}{PQ}=\frac{RP}{PQ}$

$RN=\frac{RP\times PQ}{PQ}=RP$

MN=QP

RN=RP

RN+NM=RP+PQ

RM=RQ

Angle M=Angle Q=65 degrees

Angle made by two equal sides are equal.

In triangle RMQ

$\angle R+\angle M+\angle Q=180^{\circ}$

By using triangle angles sum property

Substitute the values then we get

$\angle R+65+65=180$

$\angle R+130=180$

$\angle R=180-130=50^{\circ}$

$\angle R=50^{\circ}$

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https://brainly.in/question/4559487:Answered by Amitnrw