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˚.
Given:
<EGO = 71˚
<OEG = 90˚ (the angle forms a right angle because line EG is perpendicular to point O)
To Solve:
⇒ 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˚
Answer: <OGE (also m˚) = 19˚
Answer:
<OAC (also x˚) = 50˚
<OCB (also y˚) = 90˚
Step-by-step explanation:
–How to solve for <OCB (also y˚)
Just by looking, you can already tell that <OCB equals 90˚ because it forms a right angle.
Answer: <OCB (also y˚) = 90˚
–How to solve for <OAC (also x˚)
Given (and what we can already know):
<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˚.
To Solve:
⇒ 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˚
Answer: <OAC (also x˚) = 50˚
I hope you understand and that this helps with your question! :)
