IN THE GIVEN figure the lines AB,CD,EF INTERSECT AT POINT O. IF ANGLE BOD=X°,ANGLE AOE=2X° AND ANGLE COF=90°,FIND THE ANGLE AOE AND ANGLE AOC.
Answers
Answer:
is given that ∠BOD=180
o
from the figure we know that ∠BOD and ∠AOC are vertically opposite angles
∠AOC=∠BOD=40
o
It is given that ∠AOE=35
o
from the figure we know that ∠BOF and ∠AOE are vertically opposite angles
∠AOE=∠BOF=35
o
from the figure, we know that AOB is a straight line
so it can be written as
∠AOB=180
o
we can write it as
∠AOE+∠EOD+∠BOD=180
o
by substituting the values
35
o
+∠EOD+40
o
=180
o
∠EOD=105
o
from the figure, we know that ∠COF and ∠EOD are
vertically opposite angles
∠COF=∠EOD=105
o
Answer:
AOE = 60 degree, AOC = 30 degree
Step-by-step explanation:
Angle EOD = Angle FOC (Vertically Opposite Angles)
So, Angle EOD = 90 degree
Angle EOA + Angle EOD + Angle DOB = 180 degree (supplementary angles)
So, 2x + x + 90 = 180
3x = 90
x = 30
Therefore, angle x is equal to 30 degree.
Angle AOE = 2 x 30 = 60 degree
Angle AOC = 180 - (90 + 60) [Supplementary Angles]
= 180 - 150
= 30 degree