Answer with explanation:
Given: SA is the perpendicular bisector of TR. m∠T SR=120°.
Solution:
Let Diagonal , SA and RT intersect at point O.
In Δ S R O and Δ S TO
R O=TO=8 ft
∠SOT=∠S OR=90°----------[Given]
Side, SO is Common.
⇒Δ S R O ≅ Δ S TO-----[S A S]
∠T SA=∠R SA-----[C PCT]
But ,∠T SR=120°------[Given]
∠T SA+∠R SA=120°
2∠T SA=120°
∠T SA =60°
∠T SA =∠R SA=60°
SA is the angle bisector of ∠TSR.
⇒⇒Similarly,Using S AS
Δ RA O ≅ Δ TAO
And, ∠T A O=∠R A O-----[C PCT]
SA is the angle bisector of ∠TAR
Also, SA is the perpendicular bisector of TR.
⇒ ∠SOT=∠S OR=90°
⇒∠R O A=∠A OT=90°, because SA is a line.
∠S OR +∠R O A=180°-------[By Linear Pair]
which gives, ∠R O A=90°=∠A OT
Option C:⇒SA is the angle bisector of ∠TAR
