Question

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The question asks to find the measure of LAOC given that OC is the angle bisector of LAOB and LAOB = 84°. This is a Calculation-Based Question.
Understand the definition of an angle bisector.
An angle bisector is a ray that divides an angle into two congruent adjacent angles. In this case, OĆ bisects LAOB , which means LAOC = LBOC
2 Apply the angle bisector property to find the measure of LAOC
Since OỞ bisects LAOB, the measure of LAOC is half the measure of LAOB
1
LAOC =2<AOB
3 Substitute the given value of LAOB and calculate LAOC
Given that LAOB = 84°
, we can substitute this value into the equation:
1
LAOC =
= × 84°
2
LAOC = 42°
Therefore, the measure of LAOC is 42°
• This corresponds to the second option.

Answer 1

To find the measure of angle LAOC, given that OC is the angle bisector of angle LAOB, which measures 84°, we first recall the definition of an angle bisector: it is a ray that divides an angle into two congruent adjacent angles. Since OC bisects LAOB, we have LAOC equal to LBOC. By applying the angle bisector property, we find that LAOC is half the measure of LAOB. Thus, LAOC = 1/2 * LAOB. Substituting the given value of LAOB, we get LAOC = 1/2 * 84° = 42°. Therefore, the measure of LAOC is 42°, corresponding to the second option.