Here, since the two sides are congruent, angles c and d are equivalent. So, angle b is 47 degrees.
First, we need to find the measure of angle A. The total of all angles in a triangle is 180 degrees. So, looking at the bigger triangle, we can make an equation, knowing that c and d = 47 degrees each.
47 + 47 + a = 180
94 + a = 180
-94 -94
a = 86
Now, we know that angle A is 86 degrees. We can see that angle y is half of angle A, since there is an angle bisector that splits angle A in half. Thus, angle y is half of angle A.
Since angle A is 86 degrees, half (angle y) is 43 degrees.
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Y = 43 degrees
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Now we know 2 out of 3 of the angle measures of the smaller triangle on the left. Again, the sum of the angles of the triangle is always 180 degrees. We know that B = 47 like mentioned before, and y = 43 like we just figured out. We can make an equation:
43 + 47 + x = 180
90 + x = 180
-90 -90
x = 90
This even makes sense since angle x appears to be a right angle, and is after our calculations.
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X = 90 degrees
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Hope this helps! :)
