Question

Observe the figure, and find the measures of ∠PRS and ∠RTS.

Answer 1

Answer:

∠PRS is an exterior angle of ∆PQR. So from the theorem of remote interior angles,

∠PRS = ∠PQR + ∠QPR

= 40° + 30°

∴ ∠PRS = 70°  

∴ ∠TRS=70° …

In ∆RTS,  ∠TRS + ∠RTS + ∠TSR = 180°

[Sum of the measures of the angles of a triangle is 180°]

∴ 70° + ∠RTS + 20° = 180°

∴ ∠RTS + 90° = 180°  

∴ ∠RTS = 180°  

∴ ∠RTS = 90°

I hope it helps you☺..

Answer 2

Answer:

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