Ray AD is the angle bisector of angle ABC. m∠ABC is 168°What is the measure of ∠DBC?
I suppose the ray is BD and not AD.
An angle bisector (ray BD) divides a given angle into two equal parts.
You can take it from there.
Hint: the answer will be apparent if you draw a diagram. This works for all geometry problems.
24degrees
Says erong
Says wrong
I'm late but the quick check answers for connexus are
B- BD
C- 15
A- 2
C- 40
C- 47
100% yw
To find the measure of ∠DBC, we can use the angle bisector theorem, which states that the angle bisector of an angle divides the opposite side into two segments that are proportional to the lengths of the other two sides.
In this case, the angle bisector AD divides side BC into two segments, BD and DC. Let's denote the length of BD as x and the length of DC as y.
According to the angle bisector theorem, we have:
BD/DC = AB/AC
Since AD is the angle bisector of angle ABC, we know that AB/AC = BD/DC.
Now, we need to find the values of BD and DC. We can do this by setting up an equation using the given information.
Since m∠ABC is 168°, we know that m∠ABD + m∠DBC = 168° (using the Angle Addition Postulate).
Since AD is the angle bisector, we also know that m∠ABD = m∠DBC (using the definition of an angle bisector).
Substituting m∠DBC for m∠ABD in the equation, we get:
m∠DBC + m∠DBC = 168°
2m∠DBC = 168°
Dividing both sides by 2, we get:
m∠DBC = 168° / 2
m∠DBC = 84°
Therefore, the measure of ∠DBC is 84°.