Question

calculate the angle marked with small letters in the following diagrams​

Answer 1

Answer:

a = 51

b = 51

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Step-by-step explanation:

lets find a first.

to do so, we will first have to find the following angles:

ACB, CXY.

angle C = 90 because this is a square. The diagonal CA bisects this angle, meaning ACB is 45 degrees.

angle CXY is 84 degrees because it is opposite to AXD.

now, according to the angle sum property of triangles, the sum of all the angles of the triangles is always 180 degrees. so,

180 = a + 84 + 45

180 = a + 129

180 - 129 = a

a = 51

to find b, we need to find CDY, because CDY + b = 90 degrees, since they form one of the right angles of the square. to find CDY, we will, again, use the angle sum property of triangles.

180 = CDY + a + YCD

180 = CDY + 51 + 90

180 = CDY + 141

CDY = 180-141

CDY = 39.

CDY + b = 90

39 + b = 90

b = 90-39

b = 51