Question

Prove that the bisectors of two adjacent supplementary angles include a right angle.
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Answer 1

Answer:

it is a rule bro ...............

Answer 2

let angle EOA and angle EOB be adjacent supplementary angles.

let OC bisect angle EOA and OD bisect angle EOB

let EO be the common arm

to prove: bisectors of the two adjacent

supplementary angles include a

right angle. (i.e. angle COD = 90°)

proof:

since OC and OD bisect angle EOA and angle EOB respectively

hence, let

angle COA = angle COE = x ... (i)

and

angle DOB = angle DOE = y ... (ii)

now,

angle EOA + angle EOB = 180°

... (they're supplementary, given)

(angle COA + angle COE) + (angle DOB + angle DOE) = 180°

(x + x) + (y + y) = 180° ... (from i and ii)

2x + 2y = 180°

dividing throughout by 2, we get

x + y = 90°

angle COE + angle DOE = 90° ... (from i and ii)

angle COD = 90°

Hence, bisectors of adjacent supplementary angles include a right angle.

... Hence Proved!