Find the values of x and y in the diagram below. (4x7) 86° (7y1)⁰ (9x + 4)
Question
(4x7)
86°
(7y1)⁰
(9x + 4)
2 Answer

1. User Answers Acyclics
Answer:
x = 15 and y = 6
Stepbystep 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

2. User Answers jesscmheasley
Answer:
x = 15
y = 6
Stepbystep explanation:
The outside angle equals the measurement of the two angles farthest from it.
86 + 4x 7 = 9x + 4 Combine like terms
79 + 4x = 9x + 4 Subtract 4x from both sides
79 = 5x + 4 Subtract 4 from both sides
75 = 5x Divide both sides by 5
15 = x
The sum of the interior angels of a triangle is 180
86 + 4x 7 + 7y  1 = 180 Substitute in 15 for x
86 + (4)(15) 7 + 7y 1 = 180
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