srilakshmit
srilakshmit srilakshmit
  • 16-10-2020
  • Mathematics
contestada

Find x. Give reasons to justify your solution. b Lines AB and CD are straight lines.

Find x Give reasons to justify your solution b Lines AB and CD are straight lines class=

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akposevictor
akposevictor akposevictor
  • 21-10-2020

Answer:

x = 28

Step-by-step explanation:

Given that lines AB and CD are straight lines that intersects at O, it follows that the pair of opposite vertical angles formed are congruent.

Thus,

<AOD = <BOC

<AOD = 152°

<BOC = 3x + x + (x + 12) (angle addition postulate)

<BOC = 5x + 12

Since <AOD = <BOC, therefore,

152° = 5x + 12 (substitution)

152 - 12 = 5x (subtraction property of equality)

140 = 5x

140/5 = x (division property of equality)

28 = x

x = 28

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