Answer:
80° , 100°, 80°
Step-by-step explanation:
∠ 1 and ∠ 2 form a straight line and sum to 180° , then
2x + 40 + 2y + 40 = 180
2x + 2y + 80 = 180 ( subtract 80 from both sides )
2x + 2y = 100 → (1)
∠ 1 and ∠ 3 are vertical angles and are congruent , then
2x + 40 = x + 2y ( subtract x from both sides )
x + 40 = 2y ( subtract 40 from both sides )
x = 2y - 40 → (2)
Substitute x = 2y - 40 into (1)
2(2y - 40) + 2y = 100
4y - 80 + 2y = 100
6y - 80 = 100 ( add 80 to both sides )
6y = 180 ( divide both sides by 6 )
y = 30
Substitute y = 30 into (2)
x = 2(30) - 40 = 60 - 40 = 20
Thus x = 20 and y = 30
Then
∠ 1 = 2x + 40 = 2(20) + 40 = 40 + 40 = 80°
∠ 2 = 2y + 40 = 2(30) + 40 = 60 + 40 = 100°
∠3 = x + 2y = 20 + 2(30) = 20 + 60 = 80°
Answer:
Option (1)
Step-by-step explanation:
From the triangles given in the picture,
Since, JK ≅ KL [Given]
JM ≅ ML [Given]
KM ≅ KM [Reflexive property of congruence]
ΔJMK ≅ ΔLMK [SSS property of congruence]
Therefore, ∠JKM ≅ ∠LKM [CPCTC]
(2x + 5) = (3x - 6)
3x - 2x = 5 + 6
x = 11
m∠JKL = m∠JKM + m∠LKM
= (2x + 5) + (3x - 6)
= 5x - 1
= 5(11) - 1
= 54
Option (1) will be the answer.
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I think it's 21% when rounded to a whole number
