Find the unknown sizes of angles in the following figure (I need step by step explanation and i might give brainliest):

x = 54° , y = 29°

Step-by-step explanation:

The sum of the 3 angles in Δ ABC = 180° then

x = 180° - (72 + 54)° = 180° - 126° = 54°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of Δ CQR , then

y + 25° = x

y + 25° = 54° ( subtract 25° from both sides )

y = 29°

x = 54

y = 29

Step-by-step explanation:

First, find the magnitude of x. To do this, add the angles inside triangle ABC, which means to add 72 + 54 + x which is equal to 180 because of the rule, the sum of the interior angles of a triangle is 180. So, when the equation is simplified, you get the answer as x = 54. Then, find the magnitude of y. The magnitude of an angle drawn around a point on a straight line is always 360, and the magnitude of the same point, but only on one side of the straight line is always 180. So, we can say that the unnamed angle in the triangle CQR is 180-x, which means 180-54 because we got x as 54 earlier. Therefore, the magnitude of the unnamed angle is 126. Now, apply the same rule we used before, the sum of the interior angles of a triangle is 180, to the triangle QCR. 25 + 126 + y = 180. When this is simplified, 29 is obtained.

To find x,

 72 + 54 + x = 180 (the sum of the interior angles of a triangle is 180)

        126 + x = 180

126 + x - 126 = 180 - 126

                  x = 54

To find y,

25 + 126 + y = 180

         151 + y = 180

 151 + y - 151 = 180 - 151

                  y = 29