Question

Question #e3694

Answer 1

see explanation.

Explanation:

a) given that `DCE` is tangent to the circle, `=> angleDCO=90^@`,
`=> angleOCE=180-90=90^@`

b) recall that from the tangent-chord theorem, the angle between a tangent and a chord that meet on a circle, is equal to the inscribed angle on the opposite side of the chord,
`=> angleBAC=angleBCD=70^@`

c) recall that the angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at the circumference,
`=> angleBOC=2xxangleBAC=2xx70=140^@`

d) recall that the sum of the interior angles of a quadrilateral is `360^@`,
`=> angleBDC=360-angleBOC-angleDBO-angleDCO`
`=360-140-90-90=40^@`