given:
ab = bc
angle bdc = 371/2°
∠cbd=
37.5
105
60

Question

Accepted Answer

# Explanation:
## Step1: Use the property of triangle $ABD$
Since $\angle A = 60^{\circ}$ and $\angle ABD=60^{\circ}$, triangle $ABD$ is an equilateral triangle. So $AB = BD$.
## Step2: Use the given $AB = BC$
Because $AB = BC$ and $AB = BD$, we have $BD=BC$.
## Step3: Use the angle - sum property of a triangle
In $\triangle BDC$, if $BD = BC$, then $\angle BDC=\angle C = 37.5^{\circ}$. By the angle - sum property of a triangle ($\angle BDC+\angle C+\angle CBD = 180^{\circ}$), we substitute $\angle BDC = 37.5^{\circ}$ and $\angle C=37.5^{\circ}$ into the formula:
$$
\begin{align*}
\angle CBD&=180^{\circ}-(37.5^{\circ}+ 37.5^{\circ})\
&=105^{\circ}
\end{align*}
$$

# Answer:
$105$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of triangle \(ABD\)

Step2: Use the given \(AB = BC\)

Step3: Use the angle - sum property of a triangle

Answer: