O level A Maths syllabus include an obscure theorem called Alternate-Segment theorem, under the topic "Proofs in Plane Geometry". Alternate-Segment theorem is also known as Tangent-Chord theorem.

Alternate-Segment theorem states that when you have a chord and tangent together, as in BE and PEQ, the angle between the chord and tangent is equal to the angle in the alternate segment (segment on the other side of the chord)
thus,
angle BEQ = angle BAE = 95
angle BEP = 180 - 95 = 85

by Alternate-Segment theorem, it also means
angle BEP = angle BCE = angle BDE
angle AEP = angle ABE = angle ACE = angle ADE

proof of alternate segment theorem

consider line from E, passing through center of circle and extending to point F on circumference on other side.

angle AFE
= 180 - angle FAE - angle FEA (sum angle of triangle)
= 180 - 90 - angle FEA (angle FAE = 90; semicircle)
= 90 - angle FEA
= angle AEP (FE perpendicular to PE)

... and ...

angle ABE = angle AFE (angle in same seg)

therefore, angle AEP = angle ABE