Question

design camila is designing a new image for her cell phone case. if ( mangle abc = 35^{circ}), ( mangle bac = 29^{circ}), and ( angle acbcongangle deb), what is ( mangle deb)?

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle ABC\), we know that \(m\angle ABC + m\angle BAC+m\angle ACB=180^{\circ}\).

Step2: Substitute the given values

Given \(m\angle ABC = 35^{\circ}\) and \(m\angle BAC = 29^{\circ}\). Then \(35^{\circ}+29^{\circ}+m\angle ACB = 180^{\circ}\).
First, calculate \(35 + 29=64\). So, \(64^{\circ}+m\angle ACB=180^{\circ}\).

Step3: Solve for \(m\angle ACB\)

Subtract \(64^{\circ}\) from both sides of the equation: \(m\angle ACB=180^{\circ}- 64^{\circ}=116^{\circ}\).

Step4: Use the congruent angle property

Since \(\angle ACB\cong\angle DEB\), then \(m\angle DEB=m\angle ACB\).

Answer:

\(116\)