Angle Bisector Problem: Calculate ABC Using 65° Triangle

Angle Bisector Properties with Triangle Calculations

BD is a bisector.

What is the size of angle ABC?

656565AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate angle ABC
00:03 Angle bisector according to the given data
00:10 Angle size according to the given data
00:14 The entire angle equals the sum of its parts
00:25 Let's substitute appropriate values and solve to find angle ABC
00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

BD is a bisector.

What is the size of angle ABC?

656565AAABBBCCCDDD

2

Step-by-step solution

Since we are given that the value of angle DBC is 65 degrees, and we know that the angle bisector divides angle ABC into two equal angles, we can calculate the value of angle ABC:

65+65=130 65+65=130

3

Final Answer

130

Key Points to Remember

Essential concepts to master this topic
  • Bisector Rule: An angle bisector divides an angle into two equal parts
  • Technique: If angle DBC = 65°, then angle ABD = 65° also
  • Check: Verify angle ABC = angle ABD + angle DBC = 65° + 65° = 130° ✓

Common Mistakes

Avoid these frequent errors
  • Using the given angle as the whole angle ABC
    Don't assume 65° is angle ABC = wrong answer of 65°! The 65° is only half the angle since BD bisects it. Always remember that the bisector creates two equal parts, so multiply by 2.

Practice Quiz

Test your knowledge with interactive questions

Look at the angles shown in the figure below.

What is their relationship?

\( \)αβ

FAQ

Everything you need to know about this question

What does it mean that BD is a bisector?

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A bisector is a line that cuts an angle exactly in half, creating two equal angles. So if BD bisects angle ABC, then angle ABD equals angle DBC.

How do I know which angle is 65°?

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Look at the diagram carefully! The 65° marking shows the angle DBC (from D to B to C). Since BD bisects angle ABC, the other half (angle ABD) is also 65°.

Why do I add the two angles together?

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Because angle ABC is made up of two parts: angle ABD and angle DBC. When you put them together, you get the whole angle: 65°+65°=130° 65° + 65° = 130°

What if the angle bisector wasn't given?

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Without knowing BD is a bisector, you cannot solve this problem! The bisector property is essential because it tells us the two parts are equal.

Could angle ABC be different from 130°?

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No! Since BD bisects angle ABC and creates a 65° angle, the math is definite: the whole angle must be exactly 130°. There's only one correct answer.

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