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question 1:
the two sides are both 21 making this an isoceles triangle. In an isoceles triangle not only are two sides the same, but the bottom two angles are as well.

We know a triangle has 180°. We know the top Angle is 38° and the bottom two are the same.

we can setup an equation like this
2x + 38 = 180.
Subtract 38: 2x = 142
Divide by 2: x = 71

question 2:
the hash marks on the two sides mean they are the same length. So we are dealing with an isoceles triangle again.

Since the bottom two angles are the same, we know Angle B is also 47°.
Knowing that 180° are in a triangle, and the two 47° angles make up 94°, we know the top Angle is 86°.

The two curve lines at the top represent that those angles are the same. since we know that whole top Angle is 86, we divide that by two.
86 / 2 = 43. so y = 43°

to find x, we once again know 180° in a triangle. so take the 47° from the corner and the 43° from the top to find x.
47 + 43 + x = 180
Subtract 47 & 43: x = 90



tramserran

Answer: 71

Step-by-step explanation:

The given triangle is an isosceles triangle so the base angles are congruent (equal).  So, the angles are x + x + 38. Since the sum of the angles of a triangle equal 180°, we can set up an equation to solve for x:

x + x + 38 = 180

2x + 38 = 180

      -38   -38

2x         = 142

÷2           ÷2

x          =  71

*******************************************************************************

Answer: x = 90 , y = 43

Step-by-step explanation:

The large triangle is an isosceles triangle so the base angles are congruent (equal).  So, the angles are 47 + 47 + ∠A. Since the sum of the angles of a triangle equal 180°, we can set up an equation to solve for x:

47 + 47 + ∠A = 180

    94   +  ∠A = 180

               ∠A  = 86

Since ∠A is bisected by segment AD, then y = [tex]\frac{1}{2}[/tex](86) = 43

ABD is a triangle with angles y , x, and 47.  Their sum equals 180°:

43 + x + 47 = 180

        x + 90 = 180

               x = 90

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