BD bisects <ABC.
Find m<ABD and m<ABC when BDC= 28
Is ABC a triangle?
Is D on AC ?
To find the measures of ∠ABD and ∠ABC, we need to use the property that when a line bisects an angle, it divides the angle into two equal parts.
Given that BD bisects ∠ABC, we can say that ∠ABD is equal to ∠CBD.
Also, we are given that ∠BDC is equal to 28 degrees.
To find m∠ABD, we need to determine the value of ∠CBD.
Since BD bisects ∠ABC, we know that ∠CBD is equal to ∠DBA. Therefore, to find ∠ABD, we need to find the value of ∠DBA.
To calculate ∠DBA, we need to subtract the given angle ∠BDC from a straight angle, which measures 180 degrees.
180 - 28 = 152 degrees
So, ∠DBA measures 152 degrees, and because BD bisects ∠ABC, ∠ABD is equal to ∠CBD, which is also 152 degrees.
Therefore, m∠ABD = 152 degrees.
To find m∠ABC, we can use the property that the sum of the angles in a triangle is 180 degrees.
Since we know m∠ABD = 152 degrees, we can substitute this value into the equation:
m∠ABC = m∠ABD + m∠CBD = 152 + 28
Therefore, m∠ABC = 180 degrees.
So, m∠ABD = 152 degrees and m∠ABC = 180 degrees when m∠BDC = 28 degrees.