Points B and C are marked on the sides of angle A, equal to 45

Points B and C are marked on the sides of angle A, equal to 45, and point D in the inner region of the angle, so that ABD = 95, ACD = 90. Find BDC.

1. Mark points B, C, D as indicated in the problem statement.

We got a convex quadrilateral ABCD – it is convex because it lies on one side of each line passing through its adjacent vertices.

2. It is known that the sum of the angles of such a quadrangle is 360 °.

Let’s calculate how many degrees the sum of all known angles of the quadrangle A, ABD, ACD is:

angle A + angle ABD + angle ACD = 45 ° + 95 ° + 90 ° = 230 °.

So the BDC angle is 360 ° – 230 ° = 130 °.

Answer: The BDC is 130 °.