Converse of the Theorem: Alternate Interior Angles are Equal

Q.

Question 41

In the given figure, if PQ|| RS and QR || TS, then the value of a is

(a) ${95}^{\circ }$
(b) ${90}^{\circ }$
(c) ${85}^{\circ }$
(d) ${75}^{\circ }$

Q.

In the figure given below, if OP || RS, ∠OPQ = 110^o and ∠QRS = 130^o, then ∠PQR is equal to

1. 60${}^{\circ }$

2. 65${}^{\circ }$

3. 40${}^{\circ }$

4. 45${}^{\circ }$

Q. In the given figure, AB = AC, BC = CD and $\angle$ A = ${40}^{\circ }$, find $\angle$ACD

1. ${20}^{\circ }$
2. ${25}^{\circ }$
3. ${30}^{\circ }$
4. ${35}^{\circ }$

Q. ABC is a right triangle right angled at A. D lies on BA produced and DE perpendicular to BC intersecting AC at F. If $\angle AFE={130}^{\circ }$, find
(i) $\angle BDE$ (ii) $\angle BCA$ (iii) $\angle ABC$

Q. In a square $PQRS$, an equilateral triangle $△TQR$ is formed, then $m\angle PTS$- ?

1. ${75}^o$
2. ${90}^o$
3. ${120}^o$
4. ${150}^o$

Q.

In the figure given below, if OP || RS, ∠OPQ=110^o and ∠QRS=130^o, then ∠PQR is equal to

1. 60^o

2. 65⁰

3. 45⁰

4. 40^o

Q. In the given figure, AE || BD, AC || ED and AB = AC. Find $\angle a$ in degrees.

Q. Take any point O in the interior of a triangle PQR. Is OR$+$OP$>$RP$?$
Since sum of two sides is greater than third side.