given ∠ABC is bisected by ray BD. D is interior of angle ∠ABC. m∠ABD=87. what is m∠ABC
since ABD bisects ABC, it is 1/2 as big
So ABC is 174°
By the way, since BD bisects ABD, you don't have to say that D is interior of angle ∠ABC. Where else could it be?
To find the measure of angle ABC, you can use the fact that angle ABC is bisected by ray BD.
Given that angle ABD measures 87 degrees, we know that angle ABD is half of angle ABC.
So, to find the measure of angle ABC, you can double the measure of angle ABD.
87 degrees * 2 = 174 degrees
Therefore, the measure of angle ABC is 174 degrees.
To find the measure of ∠ABC, we can use the angle bisector theorem.
According to the angle bisector theorem, if a ray bisects an angle, then it divides the angle into two congruent angles.
In this case, ray BD bisects ∠ABC, meaning that it divides ∠ABC into two congruent angles: ∠ABD and ∠CBD.
We are given that m∠ABD = 87. Since ∠ABD and ∠CBD are congruent, m∠CBD must also be 87.
To find m∠ABC, we can add the measures of ∠ABD, ∠CBD, and ∠ABC and set it equal to 180 degrees, since the angles in a triangle add up to 180 degrees.
m∠ABD + m∠CBD + m∠ABC = 180
Substituting the known values:
87 + 87 + m∠ABC = 180
Simplifying the equation:
174 + m∠ABC = 180
Subtracting 174 from both sides:
m∠ABC = 6
Therefore, the measure of ∠ABC is 6 degrees.