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Set up an equation to solve for x. ◝ 3x = 27 3x = 30 3x + 27 + 30 = 180 3x 30 27 ◜ If two angles of a ▲ are congruent, their opposite sides are congruent. ◝ 3x x = 3x = 27 27 ◜ Set up an equation to solve for x. ◝ 3x 3x = 120 3x + 120 = 180 3x + 3x + 120 = 180 ∘ 120 ∘ ◜ All ∆s have angles that add up to 180 degrees. ◝ 3x 3x + 3x + 120 = 180 ∘ 6x + 120 = 180 120 ∘ 6x = 60 x = 3x ∘ ◜ fill in the 3rd angle Set up an equation to solve for x. 6x 30 6x = 30 6x = 54 6x + 54 = 180 ∘ 120 ∘ 54 30 ∘ If two angles of a ▲ are congruent, their opposite sides are congruent. 6x 30 ∘ 6x = 54 x = 30 54 ∘ Set up an equation to solve for x. 4x = 100 4x = 80 4x + 60 + 100 + 80 = 360 80 100 ∘ ∘ 4x ∘ 60 ∘ Quadrilateral angles add up to 360 degrees. 4x + 60 + 100 + 80 = 360 80 100 ∘ ∘ 4x + 240 = 360 4x = 120 x = 4x ∘ 60 ∘ ⊾ A ABC = 120 ∘ B 2x Set up an equation to solve for x ∘ x 2x + x = 120 2x = 120 2x + x = 180 ∘ D C A B 2x ∘ 120 x ∘ ∘ 2x + x = 120 3x = 120 x = D ⊾ C ABC = 120 Segment DE is the midsegment of ∆ABC Set up an equation for x B 4x D 32 20 A 4x = 18 4x = 20 4x + 20 = 32 18 E C D is the midpoint of segment AB (the endpoints of midsegments are midpoints) Segment DE is the midsegment of ∆ABC B 4x D 20 A 4x = 20 x = Segment DE is the midsegment of ∆ABC Set up an equation to solve for x B D 32 20 2x + 6 A 18 2x +6 = 16 2x +6 = 20 2x +6 = 32 E C Segment DE is the midsegment of ∆ABC The midsegment is half the length of the parallel ∆ side B D 32 20 2x + 6 A 18 E 2x + 6 = 16 C x = 2x = 10 Set up an equation to find x 10x 30 10x = 5y 10x = 19 10x = 30 19 5y (10x does = 5y, but that equation has two variables) (move the decimal to solve) Rectangle diagonals bisect each other. 10x 19 x = 10x = 19 |