Question

Line segment AB is perpendicular to CB Ray BD disects /ABC .What is m /DBC​

Answer 1

< DBC is
`45^(0)`

Explanation:

The line segment AB perpendicular to CB implies that a right angle is formed at point B. So that, AB and CB meets at B at
`90^(0)` to each other. Since the ray BD bisects <ABC, i.e it divides <ABC into two equal parts.

Thus,

`(90^(0) )/(2)` =
`45^(0)`

Therefore, < DBC =
`45^(0)`

and < DBC = < ABD =
`45^(0)`

These two angles are said to be complementary angles. Complementary angles are set of two or more angles that add up to
`90^(0)`.

Answer 2

The measure of angle DBC is 45°.

Explanation:

You can observe a representation of the problem in the image attached.

Notice that angle ABD and DBC are congruent.

Also, those angles are complementary, which means

`\angle ABD + \angle DBC = 90\°`

And we know that
`\angle ABD = \angle DBC = x`

So,

`x+x=90\°\\2x=90\°\\x=(90\°)/(2)\\ x=45\°`

Which means that
`\angle DBC = 45\°`

Therefore, the measure of angle DBC is 45°.