in triangle abc, ad and ce are bisectors of angle a and angle c respectively. if abc=90, find aoc.
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Angle a + angle b + angle c = 180
A + 90 + c = 180
So a and c = 45
Here ad bisects a in 22 1/2 each
Same in d also
Now in triangle aoc,
A=22 1/2
D= 22 1/2
So o= 180- 22 1/22 + 22 1/2
=180-45
=135
soham321:
i have a doubt.. hoe can we assume that a and c are 45 each... cant they also be 44 and 46 or 42 and 48 etc. or is it a rule that the opposite angles are always 45 degree?
how*
U have written that ad bisects a and ce bisects c so both the angles r equal
Did u understand now
Answered by
0
The measure of ∠AOC is 135°
GIVEN
ABC is triangle
AD is the angle bisector of ∠A
CE is the angle bisector of ∠C
∠ABC = 90°
TO FIND
∠AOC
SOLUTION
In ΔABC
∠ABC = 90° (Given )
We know that,
∠ABC + ∠BCA + ∠ACB = 180° (Sum of all the interior angles of a triangle)
90° + ∠BCA + ∠BAC = 180
∠BCA + ∠BAC = 180-90 = 90° (Equation 1)
In ΔAOC
∠AOC + ∠OAC + ∠OCA = 180°
We know that,
AD and CE are the angle bisectors of ∠A and ∠C respectively
So,
OAC + ∠OCA = 45 ° (equation 2)
Therefore,
∠AOC = 180-45 = 135°
Hence, The measure of ∠AOC is 135°
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