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Angle addition postulate

Angle Addition Postulate class=

Sagot :

Answer:

  • x = 4; m(∠EFH) = 21°, m(∠EFG) = 83°
  • x = 7, m(∠WXZ) = 38°, m(∠ZXY) = 52°

Step-by-step explanation:

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m(∠EFH) + m(∠HFG) = m(∠EFG)

(5x + 1) + 62 = (18x + 11)

5x + 1 + 62 = 18x + 11

5x + 63 = 18x + 11

5x - 18x = 11 - 63

-13x = 11 - 63

-13x = -52

x = -52 ÷ (-13)

x = 4

m(∠EFH) = 5x + 1 => m(∠EFH) = 5 × 4 + 1 => m(∠EFH) = 20 + 1 => m(∠EFH) = 21°

m(∠EFG) = 18x + 11 => m(∠EFG) = 18 × 4 + 11 => m(∠EFG) = 72 + 11 => m(∠EFG) = 83°

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A right angle is 90°.

m(∠WXZ) + m(∠ZXY) = m(∠WXY)

(5x + 3) + (8x - 4) = 90

5x + 3 + 8x - 4 = 90

13x + 3 - 4 = 90

13x - 1 = 90

13x = 90 + 1

13x = 91

x = 91 ÷ 13

x = 7

m(∠WXZ) = 5x + 3 => m(∠WXZ) = 5 × 7 + 3 => m(∠WXZ) = 35 + 3 => m(∠WXZ) = 38°

m(∠ZXY) = 8x - 4 => m(∠ZXY) = 8 × 7 - 4 => m(∠ZXY) = 56 - 4 => m(∠ZXY) = 52°

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