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Problem 3

Explanation: The angles opposite the congruent sides, are congruent angles. We consider these the base angles. This triangle is isosceles.

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Problem 4

Explanation:

Refer to the diagram below. Note how I've added in the variable y and marked another angle as 53 degrees which is one of the base angles of the left triangle. The base angles of the triangle on the right are y degrees each. Also, note the vertical angles both are y.

For the left triangle, the three angles add up to 180 which means we can solve for y to go from 53+53+y = 180 to y = 74

Then the interior angles of the triangle on the right has the three angles (y,y,x) add to 180 as well. So we have y+y+x = 180 which turns into 74+74+x = 180. That solves to x = 32

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Problem 5

Explanation:

Refer to the diagram below. I've added another base angle x, and the angle 90-x is complementary to this. This is because the two pieces must add to 90.

For the triangle on the bottom, the two base angles 74 and 74, add to the third angle 90-x and we would get 180. So we solve 74+74+(90-x) = 180 to get x = 58

think about it deeply and passionately about this property

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dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3