Corresponding Angles Axiom

Q. Corresponding angles lie on the same side of transversal and in each pair one angle is an ______ angle, while the other is an ______ angle.

1. interior, acute
2. interior, obtuse
3. interior, exterior
4. exterior, supplementary

Q.

(a) Lines AB & CD are parallel and cut by a transversal t. List the alternate, corresponding, co-interior and 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. Two parallel lines l and m are by a transversal t. If the interior angles of the same side of the be (2x-8)° and (3x-7)°, find the measure of each of these angles.

Q. If AB and CD are parallel lines and EH is the transversal, then find the measure $\angle$EFB.

1. 106°
2. 116°
3. 126°
4. 136°

Q. Refer the figure below. Which of the following angles are corresponding angles?

1. $\angle$1 and $\angle$11
2. $\angle$5 and $\angle$7
3. $\angle$10 and $\angle$12
4. $\angle$14 and $\angle$15

Q.

Given two parallel lines and a transversal, which of the following pair of angles are equal?

1. Co-interior angles

2. Alternate interior angles

3. Adjacent angles

4. Alternate exterior angles

Q. Find the value of $x$ in the given figure.

1. $32$
2. $68$
3. $64$
4. $58$

Q. If AB and CD are parallel, find the value of x.

Q. In the following figure, the lines are parallel to each other as shown. Find the angles p, q, r and s.

1. $p=110°,q=70°,r=70°,s=110°$
2. $p=110°,q=70°,r=110°,s=110°$
3. $p=70°,q=110°,r=70°,s=110°$
4. $p=70°,q=70°,r=70°,s=110°$

Q.

Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal.

(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.

(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is ${40}^{\circ }$?

$\begin{array}{cccccc}Numberofspokes& 4& 6& 8& 10& 12\\ Anglebetweenapairofconsecutivespokes\left(Indegrees\right)& 90& 60& & & \end{array}$
[3 MARKS]

Q.

In the given figure, show that AB || CD

Q. In the given figure, the angles o and r are _____ angles.

1. co-interior
2. alternate exterior
3. alternate interior
4. corresponding

Q. Angles between South & West and South & East are

1. vertically opposite angles
2. complementary angles
3. making a linear pair
4. adjacent but not supplementary

Q.

Question 48

Fill in the blanks to make the statement true.

Alternate interior angles are on the ___ side of the transversal.

Q. In the given figure, AB || DC and AD || BC, and AC is a diagonal. If ∠BAC = 35°, ∠CAD = 40°, ∠ACB = x° and ∠ACD = y°, find the value of x and y

Q. When a transversal cuts two parallel lines, the number of pairs of corresponding angles formed are ______.

1. 
   5
2. 
   4
3. 
   2
4. 
   3

Q.

The measures of $\angle$2 and $\angle$3 from the given figure are and respectively.

1. 75${}^{\circ }$
2. 105${}^{\circ }$
3. 85${}^{\circ }$
4. 95${}^{\circ }$

Q.

Question 105(i)

In the given figure, PQ, RS and UT are parallel lines.

If $c={57}^{\circ }anda=\frac{c}{3}$, find the value of d.

Q.

In the given figure, show that AB || CD

Q. If a || b || c, and m is the transversal, then 1, 2 and 3 form angles.

1. corresponding
2. co-interior
3. alternate exterior

Q. Angles between South & West and South & East are

1. complementary angles
2. making a linear pair
3. adjacent but not supplementary
4. vertically opposite angles

Q.

In the given figure, find $\angle ADG$ and $\angle IEJ$. ABCD is a rectangle. [4 MARKS]

Q.

In the figure, sides $PQ$ and $RQ$ of $△PQR$ are produced to points $S$ and $T,$ respectively. If $\angle SPR={135}^{\circ }$ and $\angle PQT={110}^{\circ }$, find $2\angle PRQ.$

1. ${90}^{\circ }$

2. ${150}^{\circ }$

3. ${110}^{\circ }$

4. ${130}^{\circ }$

Q.

Question 105(ii)

In the given PQ, RS and UT are parallel lines.

If c $={75}^{\circ }anda=\frac{2}{5}c,$ find b.

Q.

AB and CD are parallel. Then $\angle$AFE is equal to _______ degrees.

___

Q. In the given figure, find the values of the angles x, y, and z :

Q. In Fig., AB || CD and AC || BD. Find the values of x, y, z.

Q. Angles between South & West and South & East are

1. vertically opposite angles
2. complementary angles
3. making a linear pair
4. adjacent but not supplementary

Q. If l || m, then which of the following shows a pair of corresponding angles ?

1. $\angle$ 1 and $\angle$ 6
2. $\angle$ 1 and $\angle$ 7
3. $\angle$ 1 and $\angle$ 5
4. $\angle$ 1 and $\angle$ 3

Q. If ST and UV are parallel lines then, $\angle$d and $\angle$h are __________ .

1. alternate exterior angles
2. co-interior angles
3. alternate interior angles
4. corresponding angles