Using the same-side interior angles theorem, the values of x and y are:
x = 80
y = 130
<h3>What is the Same-side Interior Angles Theorem?</h3>
The same-side interior angles theorem states that two interior angles on same side of a transversal are supplementary.
(x - 30) and (x + 50) are same-side interior angles, therefore:
(x - 30) + (x + 50) = 180
Solve for x
x - 30 + x + 50 = 180
2x + 20 = 180
2x = 180 - 20
2x = 160
x = 160/2
x = 80
(x - 30) + y = 180
Plug in the value of x
(80 - 30) + y = 180
50 + y = 180
y = 180 - 50
y = 130
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The third one should be your answer
|AD| = 30 - 6 = 24
The triangle ABC and the triangle BDA are similar, therefore:
Answer: Angie = 6, Jemma = 18
<u>Step-by-step explanation:</u>
Let x represent the current age of Angie
Current Age Age 5 years from now
Angie: x x + 5
Jemma: 3x 3x + 5
5 years from now the sum of their ages is 34
(x + 5) + (3x + 5) = 34
4x + 10 = 34
4x = 24
x = 6
Angle's current age is x = 6
Jemma's current age is 3x = 3(6) = 18