Question

Need helping solving.

Answer 1

Hi!

Let's start with some facts to help us solve:

All triangles have interior angles that add up to 180 degrees.Supplementary angles also add up to 180 degrees - they are angles on a straight line.

PROBLEM NUMBER ONE:

We can solve for angle HKG by using supplementary angles. The angle next to it and itself will add up to 180 degrees, as they are on a straight line.

`120 + ?=180`

`?=60`

Angle HKG is 60 degrees.

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Now, we also know that in triangles, the angles are 180 degrees. We can add up all the angles and find x:

`60+(6x-10)+(2x+10)=180`

Remove parenthesis:

`60+6x-10+2x+10=180`

Add like terms:

`8x+60=180`

Subtract 60 from both sides:

`8x=120`

Divide both sides by 8:

`x=15`

PROBLEM NUMBER TWO

We have more supplementary angles. We can find angle JHG:

`?+72=180`

`?=108`

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Now add up the interior angles of the triangle:

`4x-2+3x+4+108=180`

Add like terms:

`7x+110=180`

Subtract 110 from both sides:

`7x=70`

Divide both sides by 7:

`x=10`

PROBLEM NUMBER TWO

We have more supplementary angles. We can find angle BDC:

`?+111=180`

`?=69`

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Now add up the interior angles of the triangle:

`69+7x+5+8x-14=180`

Add like terms:

`60+15x=180`

Subtract 60 from both sides:

`15x=120`

Divide both sides by 15:

`x=8`