The measures of the angles of a triangle are shown in the figure below solve for x
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Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Jack lives on a farm and has a large backyard. the area of his rectangular backyard is of a square mile. if the width of the yard is of a mile, what fraction of a mile is the length of the rectangular backyard?

Evaluate 3(a + b + c)squared for a = 2, b = 3, and c = 4. a. 54 b. 243 c.729 add solution .