Question

1. m∠bcv = 120° and m∠bcd = 177°. find m∠vcd.
2. find m∠ijs if m∠ijk = 153° and m∠sjk = 125°.
3. m∠efg = 112° and m∠efa = 80°. find m∠afg.

Explanation:

7.

Step1: Recall angle - addition property

We know that \(m\angle BCV+m\angle VCD=m\angle BCD\).

Step2: Rearrange the formula to find \(m\angle VCD\)

\(m\angle VCD=m\angle BCD - m\angle BCV\).

Step3: Substitute the given values

Given \(m\angle BCV = 120^{\circ}\) and \(m\angle BCD=177^{\circ}\), then \(m\angle VCD=177^{\circ}- 120^{\circ}=57^{\circ}\).

Step1: Recall angle - addition property

We know that \(m\angle IJS + m\angle SJK=m\angle IJK\).

Step2: Rearrange the formula to find \(m\angle IJS\)

\(m\angle IJS=m\angle IJK - m\angle SJK\).

Step3: Substitute the given values

Given \(m\angle SJK = 125^{\circ}\) and \(m\angle IJK = 153^{\circ}\), then \(m\angle IJS=153^{\circ}-125^{\circ}=28^{\circ}\).

Step1: Recall angle - addition property

We know that \(m\angle EFA+m\angle AFG=m\angle EFG\).

Step2: Rearrange the formula to find \(m\angle AFG\)

\(m\angle AFG=m\angle EFG - m\angle EFA\).

Step3: Substitute the given values

Given \(m\angle EFG = 112^{\circ}\) and \(m\angle EFA = 80^{\circ}\), then \(m\angle AFG=112^{\circ}-80^{\circ}=32^{\circ}\).

Answer:

\(57^{\circ}\)

8.