Question

if ( mangle acb = 180^{circ} ), and ( mangle dcb = 135^{circ} ), then ( mangle acd=) ?

Explanation:

Step1: Use the angle - addition postulate

We know that \(\angle ACB=\angle ACD+\angle DCB\) (by the angle - addition postulate, since \(\angle ACB\) is a straight angle and \(\angle ACD\) and \(\angle DCB\) form \(\angle ACB\)).

Step2: Solve for \(\angle ACD\)

Given \(m\angle ACB = 180^{\circ}\) and \(m\angle DCB=135^{\circ}\). Substitute into the equation \(m\angle ACB=m\angle ACD + m\angle DCB\). Then \(m\angle ACD=m\angle ACB - m\angle DCB\).

Substitute the values: \(m\angle ACD = 180^{\circ}-135^{\circ}\)

$$m\angle ACD=45^{\circ}$$

Answer:

\(45\)