Exercise 5.1

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°

3x° + 42° = 180°

3x° = 180° – 42^o = 138^o

x° = 138° / 3 = 46^o

x = 46°

iii) ∠ AOC + ∠ BOC = 180°

4x° + 2x° = 180°

6x° = 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°, 4x°, and 7x°

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

12x° = 360°

 x° = 360° / 12 = 30^o

 x° = 30^o

4x° = 4 × 30° = 120°

7x° = 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° + 2x° + 3x° + 4x° + 5x° = 360°

15x° = 360°

x° = 360° / 15 = 24°

x = 24°

The largest angle = 5x° = 5 × 24° = 120^o

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:

3x° + x° = 180°

4x° = 180°

x° = 180/4 = 45^o

x^o = 45°

x° = 45°

3x° = 3 × 45° = 135^o

y° = 3x° (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°