Selina solutions

Selina solutions

Grade 7

Lines and Angles (Including Construction of angles) | Exercise 14(A)

Question 13

Q13) Are the following pairs of angles supplementary?

(i) 139^{\circ}\ \ \ and\ 39^{\circ}

(ii) 26^{\circ}59'\ \ and\ 153^{\circ}1'

(iii) \frac{3}{10}\ \ of\ a\ right\ angle\ and\ \frac{4}{15}of\ two\ right\ angles\

(iv) 2x^{\circ}+65^{\circ}\ \ and\ 115^{\circ}-2x^{\circ}

Solution:

(i) 139° and 39° : No, these are not supplementary angles as their sum is not 180° (139° + 39° = 178°)

(ii) 26° 59’ and 153° 1’: Yes, there are supplementary angles as their sum is 180° (26° 59’ + 153° 1’ = 180°)

(iii) (3/10) of a right angle and 4/15 of two right angles

⇒ (3/10) of 90° and 4/15 of 180°

⇒ 27° and 48°: No, there are not supplementary angles as their sum is not 180° (27° + 48° = 75°)

(iv) 2x° + 65° and 115° - 2x° : Yes there are supplementary angles as their sum is 180° (2x + 65° + 115° - 2x° = 65° + 115° = 180°)

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subject-cta

Question 13

Q13) Are the following pairs of angles supplementary?

(i) 139^{\circ}\ \ \ and\ 39^{\circ}

(ii) 26^{\circ}59'\ \ and\ 153^{\circ}1'

(iii) \frac{3}{10}\ \ of\ a\ right\ angle\ and\ \frac{4}{15}of\ two\ right\ angles\

(iv) 2x^{\circ}+65^{\circ}\ \ and\ 115^{\circ}-2x^{\circ}

Solution:

(i) 139° and 39° : No, these are not supplementary angles as their sum is not 180° (139° + 39° = 178°)

(ii) 26° 59’ and 153° 1’: Yes, there are supplementary angles as their sum is 180° (26° 59’ + 153° 1’ = 180°)

(iii) (3/10) of a right angle and 4/15 of two right angles

⇒ (3/10) of 90° and 4/15 of 180°

⇒ 27° and 48°: No, there are not supplementary angles as their sum is not 180° (27° + 48° = 75°)

(iv) 2x° + 65° and 115° - 2x° : Yes there are supplementary angles as their sum is 180° (2x + 65° + 115° - 2x° = 65° + 115° = 180°)

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