Finding Angle ACB: Triangle with 20° Angle Bisector Problem

Question

AD bisects $∢BAC$ .

Calculate the size of $∢ACB$ .

00:05 Let's find angle A C B.

00:08 Since A D is an angle bisector, the angles are equal.

00:12 Remember, the sum of angles in a triangle is 180 degrees.

00:24 Let's group the terms and isolate angle B.

00:44 This is angle A.

00:48 Now, we'll use the same method in triangle A B C to find angle C.

00:58 Let's substitute the right values and solve for angle C.

01:18 And that's the solution to our problem!

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:

$ACB=180-90-20$

$ACB=70$