Question

Can you go step by step on this please, I need to write down notes for my math class.​

Answer 1

x = 32, y = 51

Explanation:

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

∠ U = ∠ N and NP = US

Require to find ∠ N

∠ N = 180° - (24 + 142)° ← sum of angles in triangle

= 180° - 166°

= 14°

Thus

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

2x = 64 ( divide both sides by 2 )

x = 32

and

NP = US

2x - y = 13 ← substitute x = 32

2(32) - y = 13

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

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

y = 51

Answer 2

x = 32, y = 51

Explanation:

You know the longest side of ΔTUS is 13m and the longest side of ΔMNP is (2x-y). Thus:

2x - y = 13 --- Equation 1

You know the sum of angles in a triangle is 360°. Two of the angles are given in ΔMNP (142° & 24°) and the remaining angle is (2x-50)°. Thus:

142 + 24 + 2x - 50 = 180

2x + 116 = 180

2x = 180 - 116

2x = 64

x = 64 ÷ 2

x = 32 --- Equation 2

Substitute x = 32 into Equation 1:

2(32) - y = 13

64 - y = 13

-y = 13 - 64

= -51

y = 51 --- Equation 3