Answer:
x = 15 and y = 6
Step-by-step explanation:
First we must find x to find y
We can find x using the exterior angle of a triangle statement
Statement : the exterior angle of a triangle is equal to the opposite interior angles (see attached image)
This means that 9x + 4 = 86 + 4x - 7
9x + 4 = 86 + 4x - 7
==> combine like terms
9x + 4 = 79 + 4x
==> subtract 4 from both sides
9x = 75 + 4x
==> subtract 4x from both sides
5x = 75
==> divide both sides by 75
x = 15
Now we plug in the value of x into the interior angle of the triangle so we can use the angles in a triangle theorem which states that the angles of a triangle add up to 180 degrees
So we have 86 + 4x - 7 + 7y - 1 = 180
86 + 4x - 7 + 7y - 1 = 180
==> plug in x = 15
86 + 4(15) - 7 + 7y - 1 = 180
==> multiply 4 and 15
86 + 60 - 7 + 7y - 1 = 180
==> combine like terms
138 + 7y = 180
==> subtract 138 from both sides
7y = 42
==> divide both sides by 7
y = 6
So we know x = 15 and y = 6
