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4.8 D) Angle in a Semicircle is a Right Angle
4.8 D) Angle in a Semicircle is a Right Angle
The next circle theorem that we are going to look at states that the angle at the circumference of a semicircle is a right angle (90°).
This will always be the case. All of the 3 angles at the circumference are 90°.
Example 1
What is the size of angle BCA? Give reasons for your working.
What is the size of angle BCA? Give reasons for your working.
The circle theorem states that the angle that is at the circumference of a semicircle is a right angle (90°). This means that angle ABC is 90°.
We now have a triangle with two known angles and the other remaining angle being the one that we are trying to find. We know that the angles inside a triangle add up to 180°. Therefore, we can create the following equation (I have let the angle that we are looking for equal x).
The first step in finding the value of x is to simplify the left side of the equation.
We find the value of x by moving the 118 from the left side of the equation to the right. We are able to do this by doing the opposite; we take 118 from both sides of the equation.
Therefore, x is equal to 62°.