Answer:
see explanation
Step-by-step explanation:
(10)
Since the triangles are congruent then corresponding sides are congruent, so
EF = BC , that is
4x - 1 = 19 ( add 1 to both sides )
4x = 20 ( divide both sides by 4 )\
x = 5
and
DE = AB , that is
y - 6 = 8 ( add 6 to both sides )
y = 14
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(11)
Since the triangles are congruent the corresponding angles are congruent, so
∠ K = ∠ Y , that is
3x - 37 = 41 ( add 37 to both sides )
3x = 78 ( divide both sides by 3 )
x = 26 , then
∠ K = 3x - 37 = 3(26) - 37 = 78 - 37 = 41°
The sum of the 3 angles in Δ ZMK = 180° then
∠ Z = 180° - (41 + 112)° = 180° - 153° = 27°
So
∠ A = ∠ Z
2y + 7 = 27 ( subtract 7 from both sides )
2y = 20 ( divide both sides by 2 )
y = 10
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(12)
Since the triangles are congruent the corresponding sides and angles are congruent
DG = BS
4x - 11 = 25 ( add 11 to both sides )
4x = 36 ( divide both sides by 4 )
x = 9
∠ T = 180° - (56 + 21)° = 180° - 77° = 103°
Then
∠ H = ∠ T
7y + 5 = 103 ( subtract 5 from both sides )
7y = 98 ( divide both sides by 7 )
y = 14
