Question

Find the value of a and b in each of the following diagrams.​

Answer 1

a=122

b=115

Explanation:

We have a hexagon inscribed of a Circle. Let use some obvious properties to solve some of the angles.

The upper triangle that includes 112 and 30, have a missing angle. We can use triangle interior Theorem to find the missing third angle.

The missing angle is 38.

The upper trapezoid is a cyclic quadrilateral. It 4 vertices touched the circle circumference. This means the opposite angles of the trapezoids are supplementary.

The lower left angle of the upper trapezoid measure is 65. Part of that angle is 38 so the other part is

`65 - 38 = 27`

Angle b forms a linear pair with the lower left angle so

`b + 65 = 180`

`b = 115`

Angle a is also a cyclic quadrilateral so

Angle a and 58 are supplementary

`58 + a = 180`

`a = 122`