Question

Q10)The measure of the
supplement of angle A is 40°
larger than twice the measure
of the complement of angle A.
What is the sum in degrees of
the measures of supplement
and complement of angle A?
​

Answer 1

Step-by-step explanation:

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Answer 2

SOLUTION:-

➡️ Let x be the measure of angle A.

Then,

➡️ supplement of angle A  =  180° - x 

➡️ complement of angle A  =  90° - x 

➡️ Given : The measure of the supplement of angle A is 40 degrees larger than twice the measure of the complement of angle of A. 

That is, 

(180° - x) is 40° more than 2(90° - x)

180 - x  =  2(90 - x) + 40

180 - x  =  180 - 2x + 40

↪ Subtract 180 from each side. 

- x  =  - 2x + 40

➡️ Add 2x to each side.

x  =  40

➡️ Then, supplement of angle A is

=  180 - x

=  180 - 40

=  140°

➡️ Complement of angle A is

=  90 - x

=  90 - 40

=  50°

➡️ The sum of supplement and complement of angle A is 

=  140° + 50° 

=  190°

➡️ So, the sum of supplement and complement of angle A is 190° degrees.