Question

solve using the angle addition postulate. assume that bd is between ab and bc. if ( mangle cbd=(x - 12)^{circ}, mangle abc = 73^{circ} ), and ( mangle abd=(x + 35)^{circ} ). find the measurements of ( angle cbd ) and ( angle abd ).

Explanation:

Step1: Apply angle addition postulate

According to the angle addition postulate, \(m\angle ABC=m\angle ABD + m\angle CBD\).
Substitute the given values: \(73=(x + 35)+(x-12)\).

Step2: Simplify the equation

Combine like - terms: \(73=(x+x)+(35 - 12)\).
\(73 = 2x+23\).

Step3: Solve for \(x\)

Subtract \(23\) from both sides: \(73-23=2x+23 - 23\).
\(50 = 2x\).
Divide both sides by \(2\): \(\frac{50}{2}=\frac{2x}{2}\).
\(x = 25\).

Step4: Find \(m\angle CBD\)

Substitute \(x = 25\) into \(m\angle CBD=(x - 12)^{\circ}\).
\(m\angle CBD=(25-12)^{\circ}=13^{\circ}\).

Step5: Find \(m\angle ABD\)

Substitute \(x = 25\) into \(m\angle ABD=(x + 35)^{\circ}\).
\(m\angle ABD=(25+35)^{\circ}=60^{\circ}\).

Answer:

The measure of \(\angle CBD\) is \(13^{\circ}\) and the measure of \(\angle ABD\) is \(60^{\circ}\).