## Finding Missing Angles of Parallelogram: What is x and y?

Geometric formulae, word problems, theorems and proofs, etc.
Hikari_Dreamer_12
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### Finding Missing Angles of Parallelogram: What is x and y?

Angle A is (2y-5) and Angle D is (x+50). The exterior angle of Angle C is (3x+20). What is x and y?
I am pretty confused with this one. I know that the opposite angles of a parallelogram equal each other, so Angle C is (2y-5). Angle C+the exterior angle of it=180, right? I tried doing this:
(2y-5)+(3x+20)=180
I plugged in (180-x) into y when I wanted to solve for x.
[2(180-x)-5]+(3x+20)=180
360-2x-5+3x+20=180
375+x=180
x=-195
I don't know how I ended up with a negative x value, and I know this won't work for the parallelogram angle. I think I did something wrong when I replaced the y with 180-x.

stapel_eliz
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I plugged in (180-x) into y when I wanted to solve for x.
On what basis did you do this? (The substitution would be justified if "x" and "y" were known to be supplementary angles, but I do not see this stipulation in the exercise...?)

What relationship exists between Angle C and the angle exterior to Angle C? What relationship exists between Angle C and Angle A? So what relationship exists between the angle exterior to Angle C and Angle D? Can you use these relationships to create some equations?

Armando
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### Re: Finding Missing Angles of Parallelogram: What is x and y

We know that the exterior angle of angle C is equal to the measurement of angle D, due to the opposite interior angle theorem.

$x + 50 = 3x + 20$

Move x coefficients to one side, all other terms to the other

$30 = 2x$

Simplify

$x = 15$

We also know that angle D and angle A are complementary (same-side interior angle theorem), so we can use this equation:

$2y - 5 + x + 50 = 180$

Substitute & simplify

$2y + 70 = 180$

Subtract and solve

$2y = 110$
$y = 55$

Let's verify our result

$2y - 5 + x + 50 = 180$

$2(55) - 5 + 15 + 50 = 180$

$110 - 5 + 75 = 180$

$180 = 180$

So there you have it. $x = 15$ and $y = 55$

aquiles
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### Re: Finding Missing Angles of Parallelogram: What is x and y

Hi guys, I know this is a very late review, but I cannot figure how y became 55
either way you solve the equation ( the original and the suggested) y is 60 and not 55