Finding Angle ACB: Triangle with 20° Angle Bisector Problem

Question

AD bisects $∢BAC$ .

Calculate the size of $∢ACB$ .

00:00 Find angle ACB

00:03 AD is an angle bisector, therefore the angles are equal

00:07 The sum of angles in a triangle equals 180

00:19 Let's group terms and isolate B

00:39 This is angle A

00:43 Now let's use exactly the same method in triangle ABC to find C

00:53 Let's substitute appropriate values and solve for C

01:13 And this is the solution to the question

Let's remember that an angle bisector divides the angle into 2 equal parts, therefore:

$BAD=DAC=20$

We should also note that we are given:

$ADB=ADC=90$

Since the sum of angles in a triangle is 180, we can determine the size of angle ACB as follows:

$ACB=180-90-20$

$ACB=70$