Question

A) 110° b) 135

C) 150
6. a) If 4x® and 5x® form a linear pair, find them.
b) If (2x - 10) and (3x + 20) are a linear pair, find them.
c)
A pair of complementary angles are in the ratio 2:3, find them.
d) The difference of complementary angles is 10°. Find the measures of the
angles.
e) Find the size of an angle which is five times its supplement.
f) Find the supplementary angles in which one angle is 40° more than the
other angle
g) If the supplement of an angle is four times its complement, find the ang
7. Let's find the sizes of unknown angles.​

Answer 1

(a)80 degrees and 100 degrees

(b)58 degrees and 122 degrees.

(c)36 degrees and 54 degrees

(d)50 degrees and 40 degrees

(e)150 degrees

(f)70 degrees and 110 degrees

(g)60 degrees

Explanation:

Definitions

• Complementary Angles are angles that add up to 90 degrees
• Supplementary angles are angles that add up to 180 degrees.

(a)

If 4x and 5x form a linear pair, then:

4x+5x=180

9x=180

x=20

The angles are 80 degrees and 100 degrees respectively.

(b)

If (2x - 10) and (3x + 20) are a linear pair, then:

2x-10+3x+20=180

5x+10=180

5x=180-10

5x=170

x=34

The angles are:

2x-10=2(34)-10=58 degrees

3x+20=3(34)+20=122 degrees.

(c)

A pair of complementary angles are in the ratio 2:3

The angles will be:

`(2)/(5) * 90^\circ =36^\circ\\(3)/(5) * 90^\circ =54^\circ`

(d)

The difference of complementary angles is 10°

Let the first angle =x

Let the second angle =y

Difference: x-y=10

Since they are complementary, x+y=90

Solving the two simultaneously

`x-y=10\\x+y=90\\-----\\2x=100\\x=50^\circ\\$Recall: $x-y=10\\50-y=10\\y=50-10\\y=40^\circ`

The two angles are 50 degrees and 40 degrees respectively.

(e)If an angle is 5 times its supplement

Let the supplement =x

The other angle =5x

Therefore:

5x+x=180

6x=180

x=30

The angle will then be: 5 X 30 =150 degrees

(f)If one angle is 40 more than the other and the two angles are supplementary

Let the first angle be x

The second angle will be: x+40

x+x+40=180

2x=180-40

2x=140

x=70

The two angles are 70 and 110 degrees respectively.

(g)

Let the angle =x

Its Supplement = 180 -x

Its complement =90 -x

The supplement of the angle is four times its complement.

180-x=4(90-x)

180-x=360-4x

4x-x=360-180

3x=180

x=60

The angle is 60 degrees.