Question

find m∠cbd. answer attempt 1 out of 2 m∠cbd = °

Explanation:

Step1: Identify isosceles triangle

Since \(BC = BD\) (the tick - marks indicate equal sides), \(\triangle BCD\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let \(\angle BCD=\angle BDC = 54^{\circ}\).

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle BCD\), if we let \(\angle CBD=x\), then \(x + 54^{\circ}+54^{\circ}=180^{\circ}\).

Step3: Solve for \(\angle CBD\)

\[

$$\begin{align*} x&=180^{\circ}-(54^{\circ}+ 54^{\circ})\\ x&=180^{\circ}-108^{\circ}\\ x& = 72^{\circ} \end{align*}$$

\]

Answer:

\(72\)