Question

Please help me Pleaseeeeeeeeee (you also need to find x)

Answer 1

m<CAB = 54°

m<ABC = 21°

m<ACB = 105°

m<DCB = 75°

Explanation:

Part 1: Solve for x

The sum of the 3 interior angles of a triangle always equals 180°.

** Take note

Lets call m<CAB, angle A.

Lets call m<ABC, angle B.

Lets call m<ACB, angle C.

Lets call m<DCB, angle D.

So A + B + C = 180

Therefore we have

`(13x-11)+(4x+1)+C=180`

We have 1 more angle.

They gave us an exterior angle to help us find angle C.

A straight line is 180°.

They gave us one of 2 angles.

So

`180-(18x-15)=C`

We can substitute
`180-(18x-15)` for
`C` in our first equation.

All together we have.

`(13x-11)+(4x+1)+(180-(18x-15))=180`
`13x-11+4x+1+180-(18x-15)=180`

Now lets simplify and solve for
`x`.

Simplify each term.

Apply the distributive property.

`13x-11+4x+1+180-(18x)--15=180`

`13x-11+4x+1+180-18x+15=180`

Simplify by adding like terms.
Add
`13x` and
`4x`.

`17x-11+1+180-18x+15=180`

Subtract
`18x` from
`17x`.

`-x-11+1+180+15=180`

Simplify by adding numbers.

Add
`-11` and
`1`.

`-x-10+180+15=180`

Add
`-10` and
`180`.

`-x+170+15=180`

Add
`170` and
`15`.

`-x+185=180`

Move all terms not containing
`x` to the right side of the equation.

Subtract
`185` from both sides of the equation.

`-x=180-185`

Subtract
`185` from
`180`

`-x=5`

Divide each term by − 1 and simplify.

`(-x)/(-1) =(-5)/(-1)`

`x=5`

Part 2: Find the numerical value of each angle

We can now substitute 5 for x into the equations from the picture.

`(13*5-11)+(4*5+1)+C=180`

Angle A is
`13x-11`

So A equals 54°

Angle B is
`4x+1`

So B equals 21°

Remember
`A + B + C = 180`. We can solve for
`C` and we get.

`C=180-A-B`

`C=180-54-21`

So C equals 105°

Remember a straight line is 180°.

We have 2 angles on the straight line. C and D

Therefore,
`C+D=180`

`D=180-C`

`D=180-105`

So D equals 75°

We can check. It gave us
`D=18x-15`

`D=18*5-15`

`D=90-15`

`D=75`