In the diagram, $A, B$ and $C$ form a straight angle. If $\triangle A D B$ is right-angled at $D$ and $\angle D B C=130^{\circ}$, what is the measure of $\angle D A B$ ?

![](https://cdn.mathpix.com/cropped/2024_04_30_d1e45f8438f865d01c92g-1.jpg?height=277&width=545&top_left_y=894&top_left_x=1359)
Since $A B C$ is a straight angle, then $\angle D B A=180^{\circ}-\angle D B C=180^{\circ}-130^{\circ}=50^{\circ}$.

Since the angles in a triangle add to $180^{\circ}$, then

$$
\angle D A B=180^{\circ}-\angle A D B-\angle D B A=180^{\circ}-90^{\circ}-50^{\circ}=40^{\circ}
$$

(Alternatively, we could note that $\angle D B C$ is an exterior angle for the triangle.

This means that $\angle D B C=\angle D A B+\angle A D B$, which gives $\angle D A B=\angle D B C-\angle A D B=$ $130^{\circ}-90^{\circ}=40^{\circ}$.

ANSWER: $40^{\circ}$