7th Maths : Term 1 Unit 5 : Geometry : Angles formed by a transversal : Exercise 5.2 : Text Book Back Exercises Questions with Answers, Solution

**Exercise 5.2**

** **

**1.
From the figures name the marked pair of angles.**

**Answer:**

**(i) **The marked angles
are exterior angles on the same side of the transversal

**(ii) **The angles are alternate exterior angles

**(iii) **The angles are corresponding angles

**(iv) **The angles are interior angles on the same side of the
transversal

**(v) **The angles are alternate interior angles.

**(vi) **The angles are corresponding angles.

** **

**2.
Find the measure of angle x in each the
following figures.**

**Answer: **

**(i) ***x* = 35° (corresponding angles)

**(ii) ***x* = 65° (corresponding angles)

**(iii) ***x* = 145° (corresponding angles)

**(iv) ***x* = 135° (corresponding angles)

**(v) ***x* = 90° (perpendicular angles)

** **

**3.
Find the measure of angle y in each the
following figures.**

**Answer:**

**(i) ***y *= 28° (alternate angles)

**(ii) ***y* = 58° (alternate exterior angles)

**(iii) ***y* = 123° (alternate angles)

**(iv) ***y* = 108° (alternate exterior angles)

** **

**4.
Find the measure of angle z in each the following figures.**

**Answer:**

**(i) ***z* + 31° = 180° (interior angles)

*z* = 180° – 31° = 149°

**(ii) ***z* + 135° = 180° (interior angles)

*z* = 180° – 35° = 45°

**(iii) ***z* + 79^{o} = 180° (exterior angles)

*z* = 180° – 79° = 101°

**(iv) ***z* + 22° = 180° (exterior angles)

*z* = 180° – 22° = 158°

** **

**5.
Find the value of angle a in each the
following figures.**

**Answer:**

**(i) **3*a* = 126°
(corresponding angles)

*a *= 42°

**(ii) **4*a* + 13 + 135° = 180°
(exterior angles)

4*a* + 148° = 180°

4*a *= 180°– 148° = 32°

*a* = 8°

**(iii) **8*a* + 29 = 45°
(alternate angles)

8*a* = 45° – 29° = 16°

*a *= 2°

**(iv) **6*a* = 90° (right angle)

*a *= 15°

** **

**6.
Find the value of angle x in both the
figures.**

**Answer:**

**(i) **2*x* + 15 = 3*x* – 40

(alternate interior angles)

3*x* – 2*x* = 15 + 40

*x* = 55°

**(ii) **2*x* – 15 + 3*x* + 20 = 180°

(exterior angles)

5*x* + 5 = 180°

5*x* = 180° – 5° = 175°

*x* = 35°

** **

**7.
Anbu has marked the angles as shown below in (i) and (ii). Check whether both of
them are correct. Give reasons.**

**Answer:**

**(i) **No since interior angles on the same side of the transversal are
supplementary.

**(ii) **No corresponding angles are equal.

** **

**8. Mention two real-life situations where we use
parallel lines.**

**Answer: **

Railway Track and front bar
in the window.

** **

**9.
Two parallel lines are intersected by a transvesal. What is the minimum number of
angles you need to know to find the remaining angles. Give reasons.**

**Answer: **

Minimum number of angles is
1. Using the concept of linear pair of angles, we can find one more angle and
by the concepts of corresponding angle and by the concepts of corresponding
angles and alternate angles (interior and exterior) we would find all other
angles.

** **

__Objective
type questions__

**10.
A line which intersects two or more lines in different points is known as**

(i) parallel lines

(ii) transversal

(iii) non-parallel lines

(iv) intersecting line

*Answer :***(ii) transversal**

**11.
In the given figure, angles ***a*** and ***b*** are**

(i) alternate exterior angles

(ii) corresponding angles

(iii) alternate interior angles

(iv) vertically opposite angles

*Answer :***(i) alternate
exterior angles**

**12.
Which of the following statements is ALWAYS TRUE when parallel lines are cut by
a transversal**

(i) corresponding angles supplementary.

(ii) alternate interior angles supplementary.

(iii) alternate exterior angles supplementary.

(iv) interior angles on the same side of the transversal
are supplementary.

*Answer :***(iv) interior
angles on the same side of the transversal are supplementary.**

**13.
In the diagram, what is the value of angle x?**

(i) 43°

(ii) 44°

(iii) 132°

(iv) 134°

*Answer :***(ii) 44°**

**ANSWERS**

**Exercise 5.2**

1. (i) The angles are exterior
angles on the same side of the transversal

(ii) The angles are alternate
exterior angles

(iii) The angles are
corresponding angles

(iv) The angles are interior
angles on the same side of the transversal

(v) The angles are alternate
interior angles

(vi) The angles are corresponding
angles

2. (i) 35° (ii) 65° (iii) 145°
(iv) 135° (v)90°

3. (i) 28° (ii) 58° (iii) 123°
(iv) 108°

4. (i) 149° (ii) 45° (iii) 101°
(iv) 158°

5. (i) 42° (ii) 8° (iii) 2° (iv)
15°

6. (i) 55° (ii) 35°

7. (i) No. Since, interior angles
on the same side of the transversal are supplementary.

(ii) No. Since Corresponding
angles are equal.

9. Minimum number of angles is 1.
Using the concept of linear pair of angles, we can find one more angle and by
the concepts of corresponding angles and alternate angles (interior and
exterior) we could find all other angles.

**Objective type questions**

10. (ii) transversal

11. (i) alternate exterior angle

12. (iv) interior angles on the
same side of the transversal are supplementary

13. (ii) 44°

Tags : Questions with Answers, Solution | Geometry | Term 1 Chapter 5 | 7th Maths , 7th Maths : Term 1 Unit 5 : Geometry

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7th Maths : Term 1 Unit 5 : Geometry : Exercise 5.2 (Angles formed by a transversal) | Questions with Answers, Solution | Geometry | Term 1 Chapter 5 | 7th Maths

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