Question

Ab and c lie on a straight line BD=CD BCD=15 BAD=5 Work out x

Answer 1

`x = 10`

Explanation:

The attachment completes the question;

From the question, we have the following given parameters

`BD = CD`

`\angle BCD = 15\deg`

`\angle BAD = 5\deg`

Required

Solve for x

Since
`BD = CD` then

`\angle CBD = \angle BCD` --- Property: Base angle of an isosceles triangle

`\angle CBD = \angle BCD = 15`

Also, ABC is a straight line;

So:

`\angle CBD + \angle DBA = 180` --- angle on a straight line

Substitute 15 for
`\angle CBD`

`15 + \angle DBA = 180`

Make
`\angle DBA` the subject

`\angle DBA = 180 - 15`

`\angle DBA = 165`

Considering triangle DBA

`\angle DBA + \angle BAD + x = 180` ---- angles in a triangle

Substitute 165 for
`\angle DBA` and 5 for
`\angle BAD`

`165 + 5 + x = 180`

Make x the subject

`x = 180 - 165 -5`

`x = 10`