Question

If ∆PQR~∆DEF angle p=65° and angle F=32° then angle Q is​

Answer 1

Answer:

∠Q = 83°

Step-by-step explanation:

∵  ∆PQR ∼ ∆DEF (given)

∴ ∠P = ∠D = 65°

  ∠Q = ∠E

  ∠R = ∠F = 32°

In ΔPQR

  ∠P + ∠Q + ∠R = 180°    —————— ( Angle Sun Property of Triangle)

  65° + ∠Q + 32° = 180°

  ∠Q = 180° - 65° - 32°

∴ ∠Q = 83°

Answer 2

Answer:

Given, ∆PQR~∆DEF

therefore,

<P = <D

<Q = <E and

<R = <F

here, <P= 65° and <F= 32° (given)

but, <R = <F => <R= 32°

now in the triangle PQR ,

<P + <Q + <R = 180°

=> 65° + <Q + 32° = 180°

=> <Q+ 97° = 180°

=> <Q = 180° - 97°

=> <Q = 83°

therefore, <Q = 83°

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