Question

Find the value of x in the figure shown.
65°
+
759
140
:
40
20
220​

Answer 1

65⁰+75⁰+x=180

(65+75)+x=180

140+x=180

x=180-140

x=40

x=40⁰

Answer 2

Answer:

In figure (i) BOC is a straight line

\angle AOC+\angle AOB∠AOC+∠AOB=180°

75° + 2x+ 65° +3x+x= 360°

5x+95° = 180°

5x= 180° - 95° =85°

x=\frac{85}{5}=x=

5

85

=17°

x= 17°

(ii) In figure (ii) angles are on a point

The sum = 360°

75° + 2x + 65° + x = 360°

6x+140° = 360°

6x= 360° - 140° =220°

x=\frac{220}{6}=\frac{110}{3}x=

6

220

=

3

110

x=\left(36\frac{2}{3}\right)x=(36

3

2

)°

x=36\frac{2}{3}x=36

3

2

(iii) In figure (iii) angles are on a point

Their sum= 360°

5x+3x+40° +120° =360°

x=\frac{200}{8}x=

8

200

=25°

x=25°