Finding Angle ACB: Triangle with 20° Angle Bisector Problem

AD bisects ∢BAC ∢BAC .

Calculate the size of ∢ACB ∢ACB .

AAABBBCCCDDD20

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Step-by-step video solution

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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!

Step-by-step written solution

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1

Understand the problem

AD bisects ∢BAC ∢BAC .

Calculate the size of ∢ACB ∢ACB .

AAABBBCCCDDD20

2

Step-by-step solution

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

BAD=DAC=20 BAD=DAC=20

We should also note that we are given:

ADB=ADC=90 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=180-90-20

ACB=70 ACB=70

3

Final Answer

70

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