Question

Answer this and get 50 points.​

Answer 1

15°

Explanation:

Angle in arc opposite x

360 - 210 - 90 = 60

Angle on the circumference = ½(60) = 30

Considering the triangle formed with the 90° arc

Exterior angle = 90 - (180-90)/2 = 45

Exterior angle = sum of interior angles

45 = 30 + x

x = 15

Answer 2

I drew more points as uploaded picture.

We have, arc BD + 210 + 90 = 360 deg

(sum of all arcs on circle)

=> arc BD = 360 - 210 - 90 = 60 deg

Here we have angle CBD = (1/2) x arc CD = (1/2) x 90 = 45 deg

(property of angle on circle)

=> angle ABD = angle ABC - angle CBD = 180 - CBD = 180 - 45 = 135 deg

( A, B, C lie on same line => ABC = 180 deg)

Otherwise, we have:

angle BDA = (1/2) x arc BD = (1/2) x 60 = 30 deg

We have: x + angle BDA + angle ABD = 180 deg

(sum of all angles in a triangle)

=> x = 180 - angle BDA - angle ABD

=> x = 180 -135 - 30

=> x = 15 deg

Hope this helps!

:)