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3 years ago

I need help on some geometry questions

Mathematics

1 answer:

kupik [55]3 years ago

8 0

Answer: x = 40

Step-by-step explanation:

3x + x + 20 = 180 same side (consecutive) interior angles

4x + 20 = 180

4x = 160

x = 40

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Answer: x = 24

Step-by-step explanation:

6x - 24 + 2x + 12 = 180 linear pair (supplementary angles)

8x - 12 = 180

8x = 192

x = 24

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Answer: x = 16

Step-by-step explanation:

base angles of an isosceles triangle are congruent

2(2x + 15) + 6x - 10 = 180 triangle sum theorem

4x + 30 + 6x - 10 = 180

10x + 20 = 180

10x = 160

x = 16

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Let ∠1 and ∠2 represent the exterior angles in the diagram and "x" represent the same side (consecutive) interior angle with ∠1.

Then m∠1 + x = 180 same side interior angle theorem

and m∠2 + x = 180 linear pairs are supplementary

m∠1 + x = m∠2 + x transitive property

m∠1 = m∠2 subtraction property of equality

∠1 ≈ ∠2 definition of congruency

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