Question

1. given: ( mangle abc = 76^{circ}, mangle cbe = 100^{circ} ) prove: ( mangle abe = 176^{circ} ) statements ( mangle abc + mangle cbe = mangle abe ) reasons given given

Explanation:

Step1: Substitute the given values

Given \(m\angle ABC = 76^{\circ}\) and \(m\angle CBE=100^{\circ}\). Substitute into \(m\angle ABC + m\angle CBE\).
\(m\angle ABC + m\angle CBE=76^{\circ}+ 100^{\circ}\)

Step2: Calculate the sum

\(76^{\circ}+100^{\circ}=176^{\circ}\)
Since \(m\angle ABE\) is what we need to prove and from the angle - addition postulate (if two angles \(\angle ABC\) and \(\angle CBE\) are adjacent, then \(m\angle ABC + m\angle CBE=m\angle ABE\)), and we have found that \(m\angle ABC + m\angle CBE = 176^{\circ}\)

Answer:

By substituting \(m\angle ABC = 76^{\circ}\) and \(m\angle CBE = 100^{\circ}\) into \(m\angle ABC + m\angle CBE\), we get \(76^{\circ}+100^{\circ}=176^{\circ}\). Using the angle - addition postulate (if two adjacent angles are \(\angle ABC\) and \(\angle CBE\), then \(m\angle ABC + m\angle CBE=m\angle ABE\)), so \(m\angle ABE = 176^{\circ}\)