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03 – Rule 2

Angle in semi-circle is 90°:

Prove that the angle c, which is subtended at the circumference by a semicircle is 90° or a right angle.

Draw a line, one radius long to split the triangle into two isosceles triangles as shown

Mark the angles a and b for each isosceles triangles.

Work out the other angles in each triangle

Work out the angle left at the centre. 360° – (180°–2a) – (180°–2b) = 2(a+b)

Since 2(a+b) is a straight line or 180° the angle in the semi-circle is 90°

Your Turn:

Find the value of x:

Enter your answer here:

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