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:

$x=8$