BD is a bisector.
What is the size of angle ABC?
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BD is a bisector.
What is the size of angle ABC?
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:
130
Look at the angles shown in the figure below.
What is their relationship?
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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.
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°.
Because angle ABC is made up of two parts: angle ABD and angle DBC. When you put them together, you get the whole angle:
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.
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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