Question

In the given figure,PQR is a right triangle,right angled at P. QP is extended to T and TS | QR intersecting PR at N.
If anglePNS=120°,find:
¡]angleQTS
¡¡]angle PQR
¡¡¡]angleQRP






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Answer 1

Answer:

i)ANGLE QTS IS 30 DEGREES

ii)ANGLE PQR IS 60 DEGREES

iii)ANGLE QRP IS 30 DEGREES

Step-by-step explanation:

LET THE ANGLES QTS, PQR, QRP BE x, y, z RESPECTIVELY.

ii)Observe the quadrilateral PNQS. As we know the sum of the angles in a quadrilateral is 360 degrees...

90+120+90+y=360

y=360-300

therefore y, i.e angle PQR is 60 degrees.

i)Now observe triangle QTS, we know that the sum of angles in a triangle is 180 degrees.

therefore 60+90+x=180    (Note that  i have directly substituted angle PQR       as we already found it above)

x i.e angle QTS is 30 degrees.

iii)If you observe there is another triangle PQR

therefore  90+60+z=180

z i.e angle QRP is 30 degrees.

Cheers....

Answer 2

Answer:

i)ANGLE QTS IS 30 DEGREES

ii)ANGLE PQR IS 60 DEGREES

iii)ANGLE QRP IS 30 DEGREES

_________________

Step-by-step explanation:

LET THE ANGLES QTS, PQR, QRP BE x, y, z RESPECTIVELY.

ii)Observe the quadrilateral PNQS. As we know the sum of the angles in a quadrilateral is 360 degrees...

90+120+90+y=360

y=360-300

therefore y, i.e angle PQR is 60 degrees.

i)Now observe triangle QTS, we know that the sum of angles in a triangle is 180 degrees.

therefore 60+90+x=180___(Note that  i have directly substituted angle PQR       as we already found it above)

x i.e angle QTS is 30 degrees.

iii)If you observe there is another triangle PQR

therefore  90+60+z=180

z i.e angle QRP is 30 degrees.