Question

pls ans with explanation​

Answer 1

Given:-i) ABCD,is a rectangle

ii)TUVR,us Rhombus

iii)PQRS,is a parallelogram

iv) angle,UVR=14,angleMDC=31,angleTRS=42

Now, let's move on solution

In rectangle ABCD

angleABC +angleADC=180

90+31+angleADM=180

angleADM=59

also,

anglePQR+angleSRQ=180...(PQ,is parallel to SR)...i)

In triangle DQN

amgleQDN+angleQND+angleDQN=180....ii)

clearly QN is perpendicular to DC

so,

angle,QND=90,

angleQDN=31(given)

put these value in ii)

angleDQN=180-(90+31)

=180-121=59....iii)

angleMQN+angleDQN=180

angle MQN=180-59=21

so,angle MQN=21

since,TUVR,is a Rhombus

TU=UR....(all sides of Rhombus are equal)

so,from property of triangle,we can say

angleTUR=angleTRU=x(say)

angle TUR=angleUVR=114...(opposite angle of Rhombus are equal)

since,TUR,is a triangle,so we can write

x+x+114=180

2x=64

x=32

hence,anglle TUR and TRU =32

angle SRQ=angle SRT+angleTRU=32+42=74

put this value of SRQ in i) equation

anglePQR=180-74

anglePQR=106

also,

anglePQR=anglePQD+angleDQN

put DQN=59 from iii)

106=59+anglePQD

anglePQD=47

also,angle we had taken out angle PDQ=59

so,in triangle PQD

anglePQD +angleDQP+ angleDQP=180

angleQPD=180-(47+59)

angle QPD=74

angle QPD=angleQPS=74

so,

i)angleQPS=74

ii)anglePQD=47

III)angleMQN=21

{hope it helps you}