Question

its measure.
If an angle is 30° more than one half of its complement, find the measure of the angle.
. Two supplementary angles are in the ratio 4:5. Find the angles.
. Two supplementary angles differ by 48°. Find the angles.​

Answer 1

Answer:

Answer 1:

${60}^{o}$

Answer 2:

${80}^{o} \: and \: {100}^{o}$

Answer 3:

${114}^{o} \: and \: {66}^{o}$

Step-by-step explanation:

Solution 1:

$let \: the \: angle \: be \: {x}^{o}$

A.T.Q:

x = (90 - x) + 30

x = 90 + 30 - x

x + x = 120

2x = 120

$x = {60}^{o}$

Solution 2:

$let \: the \: angles \: be \: {4x}^{o \:} and \: {5x}^{o}$

A.T.Q:

4x + 5x = 180

9x = 180

$x = \frac{180}{9} = 20$

$first \: angle \: = 4x = 4 \times 20 = {80}^{o}$

$second \: angle \: = 5x = 5 \times 20 = {100}^{o}$

Solution 3:

$let \: the \: angles \: be \: {x}^{o} and \: {y}^{o}$

A.T.Q:

x - y = 48 — (a)

We know:

Sum of supplementary angles = 180

So, x + y = 180 — (b)

Adding (a) & (b):

x - y + x + y = 48 + 180

2x = 228

$x = \frac{228}{2} = {114}^{o}$

Putting value of x in (a):

114 - y = 48

114 - 48 = y

$y = 114 - 48 = {66}^{o}$