△MNP ≅ △TUS. Use the picture below to solve for the following: x, y, and m∠N.

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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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°

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step-by-step