Answer:Statement: m<ABC = m<CBDReason: m<ABC + m<CBD = 52°Step-by-step explanation:Hi Lauren! I hope you’re fine!
Well, the exercise defines that segment BC is the bisector of angle ABD (m<ABD). As you may already know, a bisector is a segment that divides the angle (in this case m<ABD) into two equal angles (m<ABC and m<CBD).
The exercise ask you to prove that the angle m<ABC = 26 °
To arrive at this answer, you must first declare that the ABC and CBD angles are the same (this is your statement).
Then, you must apply the data they give you in the slogan as the reason. That is, you know that the greater angle ABD measures 52 ° and is the sum of the angles ABC and CBD. Therefore, in the reason column you must put m<ABC + m<CBD = 52°
So your statement is: m<ABC = m<CBD (Let's call this equation 1)
And your reason is: m<ABC + m<CBD = 52° (And let's call this equation 2)
Here is the prove:
Let's start with equation 2
m<ABC + m<CBD = 52° (WE REPLACE WITH EQUATION 1 WHERE m<ABC = m<CBD)
m<ABC + m<ABC = 52°
2 * m<ABC = 52°
m<ABC = 52°/2
m<ABC = 26°I hope I've been helpful!
Regards!