Answer:
Angle 1 = 90°
Angle 2 = 53°
Angle 3 = 37°
Explanation:
(I am not the best at explanations, but I will try my best. If you have any questions even after reading through it, feel free to ask me in the comments.)
Angle 1:
Angle 1 can be calculated by 2 different methods.
The first method involves calculation.
A rule you will need to remember for this is that angles on a straight line always add up to 180°.
Since angle 1 lies on a straight line and the magnitudes of the two other angles on the line have been provided, we can find the measure of angle 1 by simply subtracting the other two angles from 180°.
180 - 37 - 53 = 90
This means angle 1 = 90°
The second method can only be used when the angles provided are around a point. The rule used for this is that opposite angles are always equal.
The angle opposite to angle 1 on the diagram measures 90°, this means angle 1 must also be 90°.
Angle 2:
Opposite angles are always equal.
Angle 2 lies opposite to an angle measuring 53°, this means angle 2 will also have a magnitude of 53°.
Angle 3:
Similar to the other two angles, Opposite angles are always equal.
Angle 3 lies opposite to an angle measuring 37°, this means angle 3 will also have a magnitude of 37°.
Bonus tip: You can check if your angles are correct through this! Angles around a point add up to 360°, this means the total sum of all the angles should be 360° (only when calculating around a point).
90 + 37 + 53 + 90 + 37 + 53 = 360