Question

in the given figure ABCD is a pentagon inscribed in a circle such that AC is a diameter and side BC is parallel to AE if BAC is equal to 50 degree find giving reasons (I) ACB (ii) EDC (iii)BEC​

Answer 1

Answer:

i) ACB = 40 degrees

ii) EDC = 40 degrees

iii) BEC = 50 degrees

Step-by-step explanation:

i) Angle ACB = 90 - 50 = 40 degrees

Explanation:

AC is a diameter. A diameter usually subtends an angle of 90 degrees at the circumference. So, angle ABC is right angled at B. The remaining two angles must add up to 90 degrees.

ii) Angle EDC = 180 - 40 = 140 degrees

Explanation:

BC is parallel to AE, so AC is a transversal

Angle ACB = Angle CAE = 40 degrees (Angles on opposite sides of a transversal are equal - Alternate or Z-angles)

AEDC is a cyclic quadrilateral, so, the opposite angles add up to 180 degrees

Meaning

Angle EDC = 180 - <CAE = 180 -  40 = 40 degrees

iii) Angle BEC = 50 degrees

Explanation:

Angle BEC and Angle BAC are subtended on the circumference by the same chord BC

Angles subtended by the same chord on a circumference are equal.