Find the value of x.%0D%0A%0D%0A%0D%0AThe triangle on the left has all 3 sides marked with single congruence marks and all 3 angles marked with single congruence arcs.%0D%0AThe second triangle shares the right side of the first triangle. %0D%0AA second side at the lower right is marked with a single congruence mark.%0D%0AThe angle formed by the two congruent sides is labeled 100 degrees. %0D%0AThe angle formed by the two sides that are not adjacent to the first triangle is labeled x degrees.%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A60%0D%0A60%0D%0A%0D%0A50%0D%0A50%0D%0A%0D%0A40%0D%0A40%0D%0A%0D%0A30
To find the value of x, we can use the fact that the measures of the angles in a triangle add up to 180 degrees.
In the first triangle, all three angles are congruent, so each angle measures (180 degrees)/3 = 60 degrees.
In the second triangle, we know that one angle is 100 degrees, and the other two angles (including the angle labeled x) must add up to (180 degrees)-100 degrees = 80 degrees.
Since the two angles are congruent, we can divide the remaining 80 degrees equally between them. So each angle measures 80 degrees/2 = 40 degrees.
Therefore, the value of x is 40 degrees.