A home has a triangular backyard. The second angle of the triangle is 5degrees more than the first angle. The third angle is 7degrees more than two times the first angle. Find the angles of the triangular yard.

42,47,91

Step-by-step explanation:

Let the first angle = x

Second angle = 5 degree more = 5 + x

3rd angle = 7 degree more than two times = 7 + 2x

NOTE : sum of angles in a triangle = 180

X + 5+ x + 7 + 2x = 180

Collect like terms

X+x+2x +5 +7 = 180

4x + 12 = 180

4x = 180 - 12

4x = 168

Divide both sides by 4

4x/4 = 168/4

X = 42 degree

First angle = 42 degree

2nd angle = 5 + x = 5+42 = 47 degree

3rd angle = 7 + 2x = 7 + 2(42)

=7 + 84 = 91 degree

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Angle 1 = 42, Angle 2 = 47, Angle 3 = 91

Step-by-step explanation:

Angle 1 = x

Angle 2 = x + 5

Angle 3 = 2x + 7

x + x + 5 + 2x + 7 = 180°

combine like terms

4x + 12 = 180°

subtract 12 from both sides

4x = 168

divide both sides by 4

x = 42

x + 5 = 47

2x + 7 = 91

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form