find the measure of the required angle

Geometry Level 1

In $\triangle ABC$ shown above, point $D$ lies on line $AC$ . Given that $AB=AD$ and $\angle ABC - \angle ACB = 30^\circ$ , find the measure of $\angle CBD$ in degrees.

15^\circ

20^\circ

10^\circ

12^\circ

18^\circ

1 solution

A Former Brilliant Member
Dec 18, 2017

$\theta + \alpha = 30 + \angle ACB$

In $\triangle DCB$ ,

$180-\alpha + \theta + \angle ACB = 180$ $\implies$ $\angle ACB = \alpha - \theta$

Substitute,

$\theta + \alpha = 30 + \alpha - \theta$ $\implies$ $2\theta = 30$ $\implies$ $\theta = \boxed{15^\circ}$

find the measure of the required angle

1 solution

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