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.

(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

Step-by-step explanation:

Definitions

(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:

(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

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.

y/x=18

step-by-step explanation:

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2