Question

Mr. Smith is putting a brick border around his irregular shaped yard. Before installing the border, he must cut the bricks to fit the angles of the garden. Use the given measures to answer the question.

m∡A=(7x-8)°
m∡B=(4x+46)°
m∡C=(5x)°
m∡D=(6x+12)°
m∡E=(x+7)°
m∡F=(5x-9)°

What are the angle measures of each vertex of the yard? Show your work.

Answer 1

see below

Explanation:

since the given figure is made up of six sides , the sum of all the interior angles can be calculated by the formula,

( n - 2) * 180°

( 6 - 2) * 180°

4 * 180°

720°

now the sum of measures of all the unknown angles would be 720° .So ,

7x - 8 + 4x + 46 + 5x + 6x + 12+ x+7+5x-9 = 720

28x + 48 = 720

28x = 720 - 48

28x = 672

x = 24

Hence ,

• ang.A = 7x - 8 = 168 - 8 = 160°
• ang.B = 4x+46 = 96+46 = 142°
• ang.C = 5x = 120°
• ang.D = 6x+12 = 144+12 = 156°
• ang.E = x + 7 = 24 + 7 = 31°
• ang.F = 5x-9 = 120-9 = 111°

and we are done!