Question

AOB is a straight line angle COD = 90 degree and Angle Boe = 75 degree if angle AOC = X Angle BOD = y and Angle AOE = 3x find the value of x and y hence find angle AOC angle BOC angle and angle AOE

Answer 1

Answer:

value of x ;angle AOC= 35°

value of y ;angle DOB= 55°

value of 3x ;angle AOE= 105°

Explanation:

We know that angle sum on a straight line is 180°

So,

$\angle \: BOE \: + \angle \: AOE \: = 180° \\ \\ \angle \: AOE= 180° - 75° \\ \\ 3x = 105° ...eq1\\ \\ \angle \: AOE = 105°$

As well as

$\angle \: AOC + \angle \: COD + \angle \: DOB = 180° \\ \\ \angle \: AOC + \angle \: DOB = 180° - 90° \\ \\ \angle \: AOC + \angle \: DOB = 90°$

from equation 1

$x = \frac{105°}{3} \\ \\ x = 35°$

$x + \angle \: DOB = 90° \\ \\35° + \angle \: DOB = 90° \\ \\ \angle \: DOB = 90° - 35° \\ \\ \angle \: DOB = 55°$

So value of x ;angle AOC= 35°

value of y ;angle DOB= 55°

value of 3x ;angle AOE= 105°

Hope it helps you.

Answer 2

Answer:

3x+72=180(linear pair)

3x=180-72

3x=108

X=36

Similarly x+y+90=180

But X=36

36+90+y=180

126 +y=180

y=54

Hope it helps you !!!!!

Please mark it as brainliest answer!!!!!

Explanation: