We have been asked to find m∠ ABD and m∠ CBD. The expression m∠ ABD is the measure of the angle between rays BA and BD. Similarly, m∠ CBD is the measure of the angle between rays BD and BC.
The sum of m∠ ABD and m∠ CBD is equal to m∠ ABC.
m∠ ABD+ m∠ CBD= m∠ ABC
It is given that m∠ ABC equals 77^(∘). Let's substitute this and the expressions given for the two smaller angles into the equation. Then we can solve for x.
Having solved the equation, we can calculate the individual angles by substituting x= 9 into the expressions for the unknown angles.
m∠ ABD &: 3( 9)+22=49^(∘)
m∠ CBD &: 5( 9)-17=28^(∘)
