Question

In the following figure, D0A = 60°, ray OE bisects DOA and ray OF
bisects EOA. Write the measures of FOA and DOE.​

Answer 1

Given:

∠D0A = 60°

ray OE bisects DOA

ray OF  bisects EOA

To find:

∠FOA and ∠DOE

Solution:

We know that,

$\boxed{\bold{\underline{Angle \:Bisector}}}:$ $\bold{ An \:angle \:bisector\:is\:a \:line\:segment\:that \: divides\:the \:angle\:into \:two\:equal \:parts}.$

Finding the measure of ∠DOE:

Since ray OE bisects ∠DOA

∴ OE is the angle bisector of ∠DOA

⇒ ∠DOE = ∠EOA

⇒ ∠DOE = ∠EOA = $\frac{1}{2} \times \angle DOA = \frac{1}{2} \times 60\° = 30\°$

Finding the measure of ∠FOA:

Since ray OE bisects ∠DOA

∴ OF is the angle bisector of ∠EOA

⇒ ∠EOF = ∠FOA

⇒ ∠EOF = ∠FOA = $\frac{1}{2} \times \angle EOA = \frac{1}{2} \times 30\° = 15\°$

Thus, the measures of the angles are:

$\boxed{\bold{\angle FOA = \underline{15\° }}}\\\\\boxed{\bold{\angle DOE = \underline{30\° }}}$

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