Find the value of x in the triangle shown below

x = 32

Step-by-step explanation:

This is an isosceles triangle since two sides have length 10. The angles opposite the congruent sides are congruent. There is an angle measuring 116 deg, and two angles measuring x. The sum of the measures of the angles of a triangle is 180.

x + x + 116 = 180

2x + 116 = 180

2x = 64

x = 32

32 degrees

Step-by-step explanation:

There are various approaches that we could use here to determine the value of x.  Note that this triangle is isosceles (it has 2 equal sides of length 10 each).  We could draw an altitude from the 27-inch side up to the vertex of the 116 degree angle and thus divide the given triangle into 2 identical smaller triangles.  The 116 degree angle is the sum of 58 and 58 degrees.  Thus, in the smaller triangle, you have 2 known angles (58 and 90) and need only subtract (58+90) from 180 degrees to obtain the value of x:  180 degrees - (58 degrees + 90 degrees) = 32 degrees (answer).

Check:  Do the angles 32 degees and 32 degrees (opposite the angle marked x) and 116 degrees add up to 180 degrees, as they must?

Is 64 + 116 = 180?   YES

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