Finding Unknown Angles

Q.

Prove that sum of angles of triangle is $180$ degree.

Q.

A triangle can have two right angles.

1. False

2. True

Q. Two angles of a triangle are ${50}^{\circ }$ and ${70}^{\circ }$. What is the measure of the third angle?

1. ${60}^{\circ }$
2. ${70}^{\circ }$
3. ${50}^{\circ }$
4. Can't be determined.

Q. FIll in the blank :
Supplement of ${87}^{\circ }$ = _____

Q.

If two angles in a triangle are 55${}^{\circ }$ and 45${}^{\circ }$, then what would be the third angle?

1. 75${}^{\circ }$

2. 80${}^{\circ }$

3. 85${}^{\circ }$

4. 120${}^{\circ }$

Q.

Question 23

Statements (I) and (II) are as given below:
I: If two lines intersect, then the vertically opposite angles are equal.
II: If a transversal intersects two other lines, then the sum of two interior angles on the same side of the transversal is ${180}^{\circ }$.

Then,
(a) both (I) and (II) are true
(b) (I) is true and (II) is false
(c) (I) is false and (II) is true
(d) both (I) and (II) are false

Q.

If AB and CD are parallel, find the measure of angle x

1. 21°

2. 15°

3. 105°

4. 51°

Q.

In the figure shown, lines l and m are parallel and lines r and t are transversals. Find x.

1. ${45}^{\circ }$

2. ${75}^{\circ }$

3. ${60}^{\circ }$

4. ${105}^{\circ }$

Q. In the given figure, if $AB||CD,\angle APQ={50}^{\circ }and\angle PRD={127}^{\circ }$, then the value of y is.

1. ${77}^{\circ }$
2. ${127}^{\circ }$
3. ${130}^{\circ }$
4. ${50}^{\circ }$

Q.

Question 40

In the given figure, PQ ||ST. Then the value of x + y is

(a) ${125}^{\circ }$
(b) ${135}^{\circ }$
(c) ${145}^{\circ }$
(d) ${120}^{\circ }$

Q. The following diagram shows parallel lines cut by a transversal.
The value of x is.

1. 40${}^{\circ }$
2. 50${}^{\circ }$
3. 60${}^{\circ }$
4. 90${}^{\circ }$

Q.

In $\Delta ABC$, $\angle B={105}^{\circ }$, $\angle C={50}^{\circ }$. Find $\angle A$.

1. ${35}^{\circ }$

2. ${20}^{\circ }$

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

4. ${25}^{\circ }$

Q.

In a $△$ABC, $\angle$ABC = ${30}^{\circ }$ and $\angle$ACB = ${45}^{\circ }$. Which is the longest side in this triangle?

1. All are same in length

2. CA

3. BC

4. AB

Q.

As shown in above figure AB and CD are two parallel lines and a line XY passes through them and intersects AB at P & CD at Q. If $\angle DQX=x^{\circ }$ then $\angle APY=$ ___.

1. ${180}^{\circ }$

2. $x^{\circ }$

3. $180-x^{\circ }$

4. $90-x^{\circ }$

Q. In the given figure, if AB || CD then, the value of x is.

1. ${235}^{\circ }$
2. ${285}^{\circ }$
3. ${75}^{\circ }$
4. ${220}^{\circ }$

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. 40^o

3. 65⁰

4. 45⁰

Q. Find all the angles of the following triangle. [3 MARKS]

Q.

If $\angle$ACD = ${90}^{\circ }$, then line segment AB is __to line segment CD.

​​

Q.

Identify the linear pair of angles in the above problem.

1. x and y

2. ∠AOX and ∠AOY

3. ∠AOX and ∠BOX

4. All of the above

Q.

Find the numerical value of (c - a) + (d - b).

1. 90°

2. 100°

3. 110°

4. 80°

Q. Find in degrees and radians the angle between the hour hand and the minute hand of a clock at half past three.

Q.

In the given figure AC is parallel to DE. Find the value of x and y.

1. $x={95}^{\circ }$

   $y={85}^{\circ }$

2. $x={80}^{\circ }$

   $y={100}^{\circ }$

3. $x={90}^{\circ }$

   $y={90}^{\circ }$

4. $x={85}^{\circ }$

   $y={95}^{\circ }$

Q. Find the angle between the minute hand and the hour hand of a clock when the time is 7:20 AM in degrees

Q. Find the value of $x^o$.

1. ${100}^o$
2. ${120}^o$
3. ${110}^o$
4. ${130}^o$

Q.

Question 88

A road crosses a railway line at an angle of ${30}^{\circ }$ as shown in the figure. Find the values of a, b and c.

Q.

(a) Lines AB & CD are parallel. Find out the alternate, corresponding, co-interior & vertically opposite angles.

(b) (i)


l and m are parallel lines and t is the transversal. Find x

(ii)


l and m are parallel lines and t is the transversal. Find x.
[4 MARKS]

Q. (a) Find the values of x the following figure if l is parallel to m and a is parallel to b.


(b) What is the value of x in the figure?

​​​​​​​[4 MARKS]

Q.

In the following figure, if $\angle P={60}^{\circ }$

Find $\angle Q$.

1. ${120}^{\circ }$

2. ${60}^{\circ }$

3. ${80}^{\circ }$

4. ${100}^{\circ }$

Q.

As shown in above figure AB and CD are two parallel lines and a line XY passes through them and intersects AB at P & CD at Q. If $\angle DQX=x^{\circ }$ then $\angle APY=$ ___.

1. $180-x^{\circ }$

2. $90-x^{\circ }$

3. ${180}^{\circ }$

4. $x^{\circ }$

Q.

Consider the figure:

If $\angle$A = ${50}^{\circ }$​, $\angle$B = ${70}^{\circ }$​. Then x+y is equal to (in degrees):

__

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

2. ${80}^{\circ }$

3. ${100}^{\circ }$

4. ${120}^{\circ }$