in triangle ABC, AB = AC and D is a point on line AC so that line BD bisects angle ABC. if BD = BC what is the measure, in degrees, of angle A?

Guest Aug 3, 2020

#1**0 **

Hi Guest,

I believe this question has already been answered by CPhill here: https://web2.0calc.com/questions/geometry-help_68

For convenience sake, I have posted it here:

1) In triangle ABC, AB=AC and D is a point on line AC so that line BD bisects angle ABC. If BD=BC, what is the measure, in degrees, of angle A?

Call the each bisected angle. a

And call angle BCA, b

And since BD = BC...then angle BDC = angle BCD = angle BCA = b

So....since AB = AC....then angle ABC = angle BCA ⇒ 2a = b ⇒ 4a = 2b

So..in triangle BDC....

a + 2b =180

a + 4a = 180

5a = 180

a = 36

And b = 2a = 72

So...in triangle ABC

Angle ABC + Angle BCA + Angle A = 180

2a + b + Angle A = 180

72 + 72 + Angle A = 180

144 + Angle A = 180

Angle A = 180 - 144 = 108°

This is **all ***CPhill's *work, so it is all his.

Mathable Aug 3, 2020