Solving for angles in diagram involving circles and triangles

[round schooner]

Please answer om founding a and b. Thanks

[zinc umbra]

(2) is solvable but (1) is unsolvable

[peak bridge]

!nosols, please.

[glass fjord]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[zinc umbra]

i can also give full explanation or just let you solve it by giving hints

we will use this diagram to solve the question

∠CAB = 2∠CDB { angle subtended by chord at the centre of the circle is twice the angle subtended by chord at circumference of the circle.}
angle is subtended by chord CB

∠CAB = 71

∠ACB = ∠ABC {Angles opp to equal sides}
As, AC = AB {equal radii}

∠ABC + ∠ACB + ∠CAB = 180 {Angle sum property of triangle}

2∠ABC + 71 = 180
2∠ABC = 109
∠ABC = 109/2 = 54.5

[peak bridge]

maybe wanna get OP's feedback first?

or not, sorry for intruding either way.

[glass fjord]

Solving for angles in diagram involving circles and triangles

[zinc umbra]

Now,
∠DAE = ∠FAB
∠FAB = 55

Now, ∠AFB = ∠ABF {Angles opp to equal sides} ---(1)
As, AF = AB {equal radii}

so we can get,
∠AFB + ∠ABF + ∠ FAB = 180
From this we get.
2∠AFB + 55 = 180
2∠AFB = 125
∠AFB = 62.5

so , ∠ABF = 62.5
∠ABF = ∠FBC + ∠ ABC
putting values of angles we get
62.5 = a + 54.5
a = 8

[zinc umbra]

∠AFB = 62.5 so ∠b = 62.5
by this theorem

(2) Hence, a = 8 and b = 62.5