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

1.	Observe the given figure and find the measures of ∠PRS and ∠RTS.
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° …[P – T – R] 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°

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° …[P – T – R]

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°

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