Question

question
in the diagram below, \\( \overline { a d } \perp \overline { d c } \\), \\( \mathrm { m } \angle c = 58 ^ { \circ } \\) and \\( \mathrm { m } \angle c a b = 77 ^ { \circ } \\). find \\( \mathrm { m } \angle d a b \\).
show \\( \angle c a b \\)
you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.
answer attempt 1 out of 2
\\( \mathrm { m } \angle d a b = \\) submit answer

Explanation:

Step1: Find $\angle CAD$

In $\triangle ADC$, since $\angle ADC = 90^{\circ}$ and $\angle C=58^{\circ}$, using the angle - sum property of a triangle ($\angle ADC+\angle C+\angle CAD = 180^{\circ}$), we have $\angle CAD=180^{\circ}-\angle ADC - \angle C$.
Substitute $\angle ADC = 90^{\circ}$ and $\angle C = 58^{\circ}$ into the formula: $\angle CAD=180^{\circ}-90^{\circ}-58^{\circ}=32^{\circ}$.

Step2: Find $\angle DAB$

We know that $\angle CAB=\angle DAB+\angle CAD$. Given $\angle CAB = 77^{\circ}$ and $\angle CAD = 32^{\circ}$, then $\angle DAB=\angle CAB-\angle CAD$.
Substitute the values: $\angle DAB=77^{\circ}-32^{\circ}$.

Answer:

$45$