Question

Find the measurements of

Answer 1

x = 12° ; m∠ABD= 54° ; m∠DBC=126°

Explanation:

∠ABD + ∠DBC = ∠ABC

Here ,

∠ABC is a straight line .

We know,

A straight angle is 180 degrees.

So,

∠ABD + ∠DBC = 180°

⇒(4x+6)° + (11x-6)° =180° [given]

⇒15x =180°

⇒x = (180/15)° [divide both sides by 15]

∴ x = 12°

Now,

∠ABD = (4x+6)° [given]

={(4 . 12) + 6 }°

=(48+6)°

=54°

And,

∠DBC = (11x-6)° [given]

={(11 .12)-6}°

=(132 - 6)°

=126°

Answer 2

For x -

180 = 4x + 6 + 11x - 6

180 = 15x

`(180)/(15)` = x

x = 12

For m∠ABD -

4(12) + 6

48 + 6

m∠ABD = 54

For m∠DBC -

11(12) - 6

132 - 6

m∠DBC = 126