Question

IN triangle TPQ, angle T=95°,angle P=65°which of tue following is true A)PQ<TQ ,B)TQ>PT>PQ, C) PQ >PT>QT , D)PQ>TQ>PT ​

Answer 1

Answer:

D) PQ > TQ > PT is the true statement

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

We have given that,

In △TPQ,

m∠T = 95°

m∠P = 65°

Now, we know that,

m∠T + m∠P + m∠Q = 180° - - [ Angle sum property of triangle ]

⇒ 95° + 65° + m∠Q = 180°

⇒ 160° + m∠Q = 180°

⇒ m∠Q = 180° - 160°

⇒ m∠Q = 20°

Now, in △TPQ,

∠T is the greatest angle ( 95° ).

∠P is smaller than ∠T ( 65° < 95° ).

∠Q is smaller than ∠P and ∠T ( 20° < 65° < 95° ).

∴ ∠T > ∠P > ∠Q

Now, we know that,

The side opposite to greater angle is greater and the side opposite to smaller angle is smaller in a triangle.

Side opposite to ∠T is PQ.

Side opposite to ∠P is TQ.

Side opposite to ∠Q is PT.

∴ PQ > TQ > PT

∴ D) PQ > TQ > PT is the true statement.

Answer 2

Given :

• T = 95°
• P = 65°

According to the question :

Sum of interior angles of a triangle = 180°

T + P + Q = 180°

Substituting the values, we have,

we get,

⟹ 95° + 65° + Q = 80°

⟹ 160° + Q = 180°

⟹ Q = 180° - 160°

⟹ Q = 20°

Verification :

⟹ T + P + Q = 180°

⟹ 95° + 65° + 20° = 180°

⟹ 160° + 20° = 180°

⟹ 180° = 180°

Since, side opposite to greater angle to Greater

∴ TP < PQ < TQ

So, It's Done !!