Answer:
x = 4, y = 6
Explanation:
∠ DEC = 112° ( vertical angle )
Since BE = CE then Δ BCE is isosceles
∠ BCE = 7x + 6 ( base angles of an isosceles Δ are congruent )
The sum of the 3 angles in a triangle = 180°, thus
112 + 7x + 6 + 7x + 6 = 180, that is
14x + 124 = 180 ( subtract 124 from both sides )
14x = 56 ( divide both sides by 14 )
x = 4
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∠ DEC = 180° - 112° = 68° ( straight angle )
Since CE= DE then Δ CDE is isosceles
∠ DCE = 9y + 2 ( base angles of an isosceles Δ are congruent )
The sum of the 3 angles = 180°, thus
68 + 9y + 2 + 9y + 2 = 180, that is
18y + 72 = 180 ( subtract 72 from both sides )
18y = 108 ( divide both sides by 18 )
y = 6