In triangle ABC if m<ABF=39 and BF is an angle bisector, find <BCE
Where is E ?
not enough information.
To find the measure of angle BCE, we need to use the angle bisector theorem.
The angle bisector theorem states that in a triangle, the angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides.
In triangle ABC, let's label the measure of angle ABF as x. Since BF is an angle bisector, angle CBF will also have a measure of x.
Using the angle sum property of a triangle, we have:
x + x + m<ACB = 180°
Simplifying this equation, we get:
2x + m<ACB = 180°
Now, let's apply the given information that m<ABF = 39°. Since angle ABF and angle CBF are congruent due to the angle bisector, we have:
2x + 39° = 180°
Subtracting 39° from both sides of the equation, we get:
2x = 180° - 39°
2x = 141°
Finally, dividing both sides of the equation by 2, we find:
x = 70.5°
Since angle BCE is congruent to angle CBF, we can conclude that m<BCE = 70.5°.