Question

if \\(m\angle acb = 180^{\circ}\\), and \\(m\angle acd = 120^{\circ}\\), then \\(m\angle dcb = \quad^{\circ}\\)

Explanation:

Apply the Angle Addition Postulate

$$ \text{m}\angle\text{ACD} + \text{m}\angle\text{DCB} = \text{m}\angle\text{ACB} $$

Substitute the given values

$$ 120^\circ + \text{m}\angle\text{DCB} = 180^\circ $$

Solve for the unknown angle

$$ \text{m}\angle\text{DCB} = 180^\circ - 120^\circ = 60^\circ $$

Answer:

If \(\text{m}\angle\text{ACB} = 180^\circ\), and \(\text{m}\angle\text{ACD} = 120^\circ\), then \(\text{m}\angle\text{DCB} =\) <blank>\(60\)</blank>\(^\circ\)