Geometry Practice Test 1

Question : 6 of 40

Marks: +1, -0

The line segments AB and CD intersect at O. OF is the internal bisector of obtuse angle BOC and OE is the internal bisector of acute angle AOC. If ∠BOC = 130°, what is the measure of ∠FOC?

90°
110°
115°
120°

Validate

Solution:

Two line segment, AB and CD intersect at O.
∠BOC = 130°
OF is the internal bisector of ∠BOC
⇒ ∠BOF = ∠COF = 65°

OE is the internal bisector of acute angle AOC
∠AOC = x
⇒ ∠AOE = ∠COE =

x/2

Now ∠AOC + ∠BOC = 180°
∠AOC = 180° −130°
∠AOC = x = 50°
∠AOE = ∠COE =

{50°}/2

= 25°
Now ∠FOE = ∠COE +∠COF
∠FOE = 25° + 65° = 90°

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