Answer:
x = 32
y = 51
m∠N = 14°
Step-by-step explanation:
Given:
ΔMNP ≅ ΔTUS
By the property of similarity,
MN ≅ TU, NP ≅ US and MP ≅ TS
m∠M = m∠T = 142°,
m∠N = m∠U = (2x - 50)°
m∠P = m∠S = 24°
Since, m∠N = [180°- (m∠M + m∠P)]
(2x - 50) = 180 - (142 + 24)
2x - 50 = 14
2x = 64 ⇒ x = 32
Since, NP = US,
2x - y = 13
2(32) - y = 13
64 - y = 13
y = 51
m∠N = 180° - (142 + 24)°
= 14°
The value is x = 32 , y = 51 , and m∠N = 14°
Given that
Based on the above information, the calculation is as follows:
Here we use the property of similarity,
So,
MN ≅ TU, NP ≅ US , and MP ≅ TS
Based on this
m∠M = m∠T = 142°,
m∠N = m∠U = (2x - 50)°
m∠P = m∠S = 24°
As
m∠N = [180°- (m∠M + m∠P)]
(2x - 50) = 180 - (142 + 24)
2x - 50 = 14
2x = 64
x = 32
As, NP = US,
2x - y = 13
2(32) - y = 13
64 - y = 13
y = 51
m∠N = 180° - (142 + 24)°
= 14°
Therefore the above are the answers.
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