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I am utterly confused on what I'm supposed to do cause my teacher says to use what we know about supplementary and complementary angles to find the answer but $126° + 58°$ would equal $184°$ which would be neither $180°$ or $90°$. So how would I solve x? If he wants use to find Supplementary or Complementary or does he want us to find any other angle cause I'm not sure if we've learned anything like Adjacent, Linear, or Vertical. Please help me. The problem is down below but I might have to put it in the comments cause it won't let me add a picture.

The Angles Problem

rogerl
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Nora Smith
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    What do you know about the angle that's next to the $126^\circ$ angle? – Robert Shore Jun 02 '22 at 00:08
  • @RobertShore I don't know...I suck at this and I am having a hard time. I think it would be acute and possibly around 20° but I'm not sure. Excatly what angle next to it? Like the inside of the triangle? – Nora Smith Jun 02 '22 at 00:11
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    @RobertShore On the work he says: Hint: You may want to find the other missing angles in the triangle first. – Nora Smith Jun 02 '22 at 00:15
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    What is the angle on the other side of the slanted line from the $126^{\circ}$ angle? (How is it related to the $126^{\circ}$ angle?) – rogerl Jun 02 '22 at 00:41
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    Yes, I mean the angle on the inside of the triangle that's next to the $126^\circ$ angle. – Robert Shore Jun 02 '22 at 01:33

1 Answers1

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Label the lower left angle inside the triangle $Y$, and the lower right angle inside the triangle $Z$.

Some hints:

  1. $Z$ is the supplement of $126^{o}$.
  2. $Y + Z + 58^{o}$ are the interior angles of a triangle, which add up to ... ?
  3. $X$ is the supplement of $Y$.

Does this help?

Spoiler:

1. $126 + Z = 180$ so $Z = 54$. 2. $54 + 58 + Y = 180$ so $Y = 180 - 54 - 58 = 68$. 3. $X + 68 = 180$ so $X = 180 - 68 = 112$.

John
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