Question

Find the value of x and y. Triangle MNP = triangle TUS

Answer 1

Answer:

x = 32, y = 51

Step-by-step explanation:

Since the triangles are congruent then corresponding sides and angles are congruent, that is

∠ U = ∠ N

∠ N = 180° - (142 + 24)° = 180° - 166° = 14° , then

2x - 50 = 14 ( add 50 to both sides )

2x = 64 ( divide both sides by 2 )

x = 32

and

NP = US

2x - y = 13

2(32) - y = 13

64 - y = 13 ( subtract 64 from both sides )

- y = - 51 ( multiply both sides by - 1 )

y = 51

Answer 2

Using the triangle theorem, the values of x and y is 32° and 51° respectively

From △MNP

∠M + ∠N + ∠P = 180° (Sum of interior angles in a triangle)

N = 180 - (142 + 24)

N = 180 - 168

N = 14°

Equate the expression :

2x - 50 = 14

2x = 14 + 50

2x = 64

x = 64 / 2

x = 32°

From ; 2x - y = 13 _____(1)

Substitute x = 32 into the expression ;

2(32) - y = 13

64 - y = 13

64 - 13 = y

51° = y

Therefore, the values of x and y is 32° and 51° respectively.

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