Question

Please can some explain how to identify angles that on the same segment? ​

Answer 1

Step-by-step explanation:

Angles in the same segment. The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.

Picture 1  a° = a°  they are the same

Picture 2  p= 52°  q= 40° Angles in the same segment are equal. if they ask you to calculate you just show both angles p= 52 and q=40.

Picture 3 + 4  Let the obtuse angle MOQ = 2x.  

Using the circle theorem, the angle at the centre is twice   the angle at the circumference.

Therefore picture 4 tells us and proves;

Angle MNQ = x and angle MPQ = x.

Picture 5

A cyclic quadrilateral is a quadrilateral drawn inside a circle. Every corner of the quadrilateral must touch the circumference of the circle.

The second shape is not a cyclic quadrilateral. One corner does not touch the circumference.

Picture 6

The opposite angles in a cyclic quadrilateral add up to 180°.

a + c = 180°

b + d = 180°

Picture 7

Example

Calculate the angles a and b.

The opposite angles in a cyclic quadrilateral add up to 180°.

This is a picture that couldn't be added but has a quadrilateral occupying half the triangle consisting of 3 arcs the middle one was 140 and proved part of one triangle. The x (a) missing angle showed below a = 180-60 = 120 °

So hopefully this will help you remember the format here for quadrilateral shapes within a circle.

b = 180 - 140 = 40°

a = 180 - 60 = 120°