Find angle ABC or angle ACB, or angle ABC = 180 - ACB - Edexcel - GCSE Maths - Question 18 - 2022 - Paper 1
Question 18
Find angle ABC or angle ACB, or angle ABC = 180 - ACB.
Substituting into the formula, we find
for angle ABC = 90 - ACB.
Angle ABC is inscribed in a semicircle ... show full transcript
Worked Solution & Example Answer:Find angle ABC or angle ACB, or angle ABC = 180 - ACB - Edexcel - GCSE Maths - Question 18 - 2022 - Paper 1
Step 1
Method to find angle ABC = 90 - ACB
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Answer
To find angle ABC, we start with the relationship that the measure of angles in a triangle summate to 180°. Using this relationship:
ABC+ACB+90=180
This allows us to rearrange for ABC:
ABC=90−ACB
Thus, angle ABC is equal to 90 degrees minus the measure of angle ACB.
Step 2
Angle at the circumference theorem
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Answer
The angle opposite the diameter in a semicircle is a right angle, which means:
ABC=90−ACB
As such, we can find angle ABC using the inscribed angle theorem, specifically pointing out that the tangent to a circle is perpendicular to the radius at the point of contact.
