7th Maths : Term 1 Unit 5 : Geometry : adjacent angles, linear pair of angles and vertically opposite angles : Exercise 5.1 : Text Book Back Exercises Questions with Answers, Solution

**Exercise
5.1**

** **

**1.
Name the pairs of adjacent angles.**

**Answer:**

The pairs of adjacent angle are

*∠** *ABG and *∠** *GBC, *∠** *BCF and *∠** *FCE

*∠** *FCE and *∠** *ECD, *∠** *ACF and *∠** *FCE

*∠** *ACF and *∠** *ECD

** **

**2.
Find the angle ****∠****JIL from the given
figure.**

**Answer:**

*∠ *JIL
= 38° + 27° = 65°

** **

**3.
Find the angle ****∠****GEH from the given
figure. **

**Answer:**

*∠* GEH
= 120° – 34° = 86°

** **

**4.
Given that ***AB*** is a straight
line. Calculate the value of ***x***° in the following cases.**

**Answer: **

**i)** *∠** *AOC + *∠** *BOC = 180°

72° + *x*° = 180°

*x***° = 180° – 72° = 108°**

**ii) ***∠** *AOC + *∠** *BOC = 180°

3*x*° + 42° = 180°

3*x*° = 180° – 42^{o}
= 138^{o}

*x*° = 138° / 3 = 46^{o}

*x*** = 46°**

**iii) ***∠** *AOC + *∠** *BOC = 180°

4*x*° + 2*x*° = 180°

6*x*° = 180°

*x*° = 180° / 6^{o} = 30^{o}

**x° = 30°**

** **

**5.
One angle of a linear pair is a right angle. What can you say about the other angle?**

**Answer:**

The other angle is also a
right angle.

** **

**6.
If the three angles at a point are in the ratio 1 : 4 : 7, find the value of each
angle?**

**Answer:**

Three angles are in the ratio 1:4:7

Let the three angles be* x*°,
4*x*°, and 7*x*°

Sum of the three angles at a point *x*° + 4*x*° + 7*x*° = 360°

12*x*° = 360°

*x*° = 360° / 12 = 30^{o}

* x*° = 30^{o}

4*x*° = 4 × 30° = 120°

7*x*° = 7 × 30° = 120°

The three angles are 30°, 120°, 210°

** **

**7.
There are six angles at a point. One of them is 45° and the other five angles are
all equal. What is the measure of all the five angles?**

**Answer:**

The sum of six angles at a point = 360°

One angle = 45°

The other five angles = 315°

The measure of each angles = 315° / 5 = 63°

** **

**8.
In the given figure, identify**

**(i)
any two pairs of adjacent angles.**

**(ii)
two pairs of vertically opposite angles.**

**Answer:**

**(i) any two pairs
of adjacent angles.**

Adjacent angles ∠ PQU and ∠ PQT

∠ PQT and ∠ TQS

∠ TQS and ∠ SQR

∠ SQR and ∠ RQU

∠ RQU and ∠ PQU

**(ii) two pairs of
vertically opposite angles.**

Vertically opposite angles

∠ PQU and ∠ TQR

∠ PQT and ∠ UQR

** **

**9.
The angles at a point are x°, 2x°, 3x°,
4x° and 5x°. Find the value of the largest angle?**

**Answer:**

Sum of the angles at a point

*x*° + 2*x*° + 3*x*° + 4*x*° + 5*x*° = 360°

15*x*° = 360°

*x*° = 360° / 15 = 24°

*x* = 24°

**The largest angle =
5 x° = 5 **×

** **

**10.
From the given figure, find the missing angle.**

**Answer:**

∠ROQ and ∠POS are vertically opposite angles.
They are equal.

∠ROQ =105°

∠POS = *x*° = 105°

** **

**11.
Find the angles x° and y° in the figure shown.**

**Answer:**

3*x*° + *x*° = 180°

4*x*° = 180°

*x*° = 180/~~4~~ = 45^{o}

*x*^{o }**= 45°**

*x*° = 45°

3*x*° = 3 × 45° = 135^{o}

*y*° = 3*x*° (vertically
opposite angles)

**y****°= 135°**

** **

**12.
Using the figure, answer the following questions. **

**(i)
What is the measure of angle x°? **

**(ii)
What is the measure of angle y°?**

**Answer:**

The measure of *x* =
125° (vertically opposite angles)

*x*° + *y*° = 180°

125^{o} + *y*^{o
}= 180°

*y*^{o} = 180° – 125° = 55°

*x*° = 125°

*y*° = 55°

** **

**Objective
type questions**

**13.
Adjacent angles have**

(i) no common interior, no common arm, no common
vertex

(ii) one common vertex, one common arm, common interior

(iii) one common arm, one common vertex, no common
interior

(iv) one common arm, no common vertex, no common
interior

*Answer : *iii) one common arm, one common vertex, no common
interior

**14.
In the given figure the angles ****∠****1 and ****∠****2 are**

(i) opposite angles

(ii) Adjacent angles

(iii) Linear pair

(iv) Supplementary angles

*Answer :*iii) Linear pair

**15.
Vertically opposite angles are **

(i) not equal in measure

(ii) complementary

(iii) supplementary

(iv) equal in measure

*Answer : *iv) Equal in measure

**16.
The sum of all angles at a point is **

(i) 360°

(ii) 180°

(iii) 90°

(iv) 0°

*Answer : *i) 360°

**17.
The measure of ****∠****BOC is**

(i) 90°

(ii) 180°

(iii) 80°

(iv) 100°

*Answer : *iii) 80°

**ANSWERS**

**Exercise 5.1**

1. The pairs of adjacent angle
are ∠ABG and ∠GBC , ∠BCF and ∠FCE , ∠FCE and ∠ECD , ∠ACF and ∠FCE , ∠ACF and ∠ECD

2. 65°

3. 86°

4. (i) 108° (ii) 46° (iii) 30°

5. The other angle is also a
right angle.

6. 30° , 120°, 210°

7. 63°

8. Adjacent angles: ∠PQU and ∠PQT , and ∠TQS , ∠TQS and ∠SQR , ∠SQR and ∠RQU , ∠RQU and ∠PQU (all possible answers)

Opposite pairs: ∠PQU and ∠TQR , ∠PQT and ∠UQR

9. 120°

10. 105°

11. 45°, 135°

12. (i) 125° (ii) 55°

**Objective type questions**

13. (iii) one common arm, one
common vertex, no common interior

14. (iii) linear pair

15. (iv) equal in measure

16. (i) 360°

17. (ii) 80°

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 5.1 | Questions with Answers, Solution | Geometry | Term 1 Chapter 5 | 7th Maths

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