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ycow [4]
2 years ago
14

Solve the following problems. Remember that all reasoning must be explained, and all steps of math work must be shown!

Mathematics
1 answer:
iris [78.8K]2 years ago
3 0

Answer to Question 1:

<OGE (also m˚) = 19˚

Step-by-step explanation:

We know that all the angles in a triangle add up to 180˚.

<u>Given:</u>

<EGO = 71˚

<OEG = 90˚ (the angle forms a right angle because line EG is perpendicular to point O)

<u>To Solve:</u>

⇒ Since we know two angles, we should know the third; and they all add up to 180˚. This can be written as:

71˚ + 90˚ + <OGE = 180˚

⇒ Solve for <OGE by simplifying:

161˚ + <OGE = 180˚

⇒ Subtract 161˚ from both sides to get:

161˚ − 161˚ + <OGE = 180˚ − 161˚

⇒ Isolate <OGE:

<OGE = 19˚

<u>Answer:</u> <OGE (also m˚) = 19˚

Answer:

<OAC (also x˚) = 50˚

<OCB (also y˚) = 90˚

Step-by-step explanation:

–<u>How to solve for <OCB (also y˚)</u>

Just by looking, you can already tell that <OCB equals 90˚ because it forms a right angle.

<u>Answer:</u> <OCB (also y˚) = 90˚

–<u>How to solve for <OAC (also x˚)</u>

<u>Given (and what we can already know):</u>

<AOC = 40˚

<OCA = 90˚

⇒ Reason: Line AB is a straight line and a straight line equals 180˚. We already know on side of the line because <OCB is 90˚, and so the other side, <OCA, should also be 90˚, since the both sides that make up the straight line equal 180˚ (90˚ + 90˚ = 180˚). You can also tell that <OCA forms a right angle in the triangle because line AB is perpendicular to point O, and right angles are 90˚.

<u>To Solve:</u>

⇒ Since we know two angles in the triangle, we should know the third; and they all add up to 180˚. This can be written as:

40˚ + 90˚ + <OAC = 180˚

⇒ Solve for <OAC by simplifying:

130˚ + <OAC = 180˚

⇒ Subtract 130˚ from both sides to get:

130˚ − 130˚ + <OAC = 180˚ − 130˚

⇒ Isolate <OAC:

<OAC = 50˚

<u>Answer:</u> <OAC (also x˚) = 50˚

I hope you understand and that this helps with your question! :)

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