3 [ Angles subtended by equal arcs and equal chords]

In a convex quadrilateral $A B C D$, it is known that $\angle C B D=58^{\circ}, \angle A B D=44^{\circ}, \angle A D C=78^{\circ}$. Find the angle $C A D$.
Quadrilateral $A B C D-$ is inscribed.

## Solution

Since

$$
\angle A B C=\angle A B D+\angle D B C=44^{\circ}+58^{\circ}=102^{\circ},
$$

Therefore, quadrilateral $A B C D$ is inscribed. Hence,

$$
\angle C A D=\angle D B C=58^{\circ}
$$

![](https://cdn.mathpix.com/cropped/2024_05_06_02603d12f3437ea52c37g-15.jpg?height=326&width=380&top_left_y=243&top_left_x=839)

## Answer

$58^{\circ}$.

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