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3 years ago

Please help!

Mathematics

1 answer:

egoroff_w [7]3 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

The diagonals of a kite are perpendicular to each other, hence

∠EHF = 90°

The sum of the 3 angles in a triangle = 180°

In ΔEHF

∠1 + ∠2 + 90 = 180, that is

42 + ∠2 + 90 = 180

132 + ∠2 = 180 ( subtract 132 from both sides )

∠2 = 48°

DE and DG are congruent sides, hence

4x - 2 = 22.5 ( add 2 to both sides )

4x = 24.5 ( divide both sides by 4 )

x = 6.125

∠A and ∠C are congruent, hence

∠A = ∠C = 82°

The sum of the interior angles of a kite = 360°, hence

x = 360 - (82 + 82 + 140) = 360 - 304 = 56

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