Question

m∠b=□°
m∠c=□°
m∠d=□°

Explanation:

Step1: Use the property of isosceles triangle

Since \(BD = BC\), \(\angle D=\angle C\). So \(\angle C=(2x + 20)^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of interior angles of a triangle is \(180^{\circ}\). So \((2x + 20)+(2x + 20)+(5x + 23)=180\).
Simplify the left - hand side: \(2x+20 + 2x+20+5x + 23=9x + 63\).
Then \(9x+63 = 180\).
Subtract 63 from both sides: \(9x=180 - 63=117\).
Divide both sides by 9: \(x = 13\).

Step3: Calculate \(\angle B\)

Substitute \(x = 13\) into \(\angle B=(5x + 23)^{\circ}\).
\(\angle B=(5\times13 + 23)^{\circ}=(65 + 23)^{\circ}=88^{\circ}\).

Step4: Calculate \(\angle C\)

Substitute \(x = 13\) into \(\angle C=(2x + 20)^{\circ}\).
\(\angle C=(2\times13+20)^{\circ}=(26 + 20)^{\circ}=46^{\circ}\).

Step5: Calculate \(\angle D\)

Since \(\angle D=\angle C\), \(\angle D = 46^{\circ}\).

Answer:

\(m\angle B = 88^{\circ}\), \(m\angle C = 46^{\circ}\), \(m\angle D = 46^{\circ}\)