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Alekssandra [29.7K]
1 year ago
9

Explain how you determined each of the numbered angle measures.

Mathematics
1 answer:
nalin [4]1 year ago
4 0

The numbered angle measured is ∠1 = 61°, ∠2= 119, ∠3 = 61, ∠4 = 119, ∠5 = 119, ∠6 = 61 , ∠7 = 119

In this figure, we have

∠8 = 61°

Now, To find the

∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7

Now, Let's take the ∠7 and ∠8

and, firstly find the ∠7

We know that the sum of two angles is 180°

and, Given the  ∠8 = 61°

∠7 + ∠8 = 180° (Linear Pair of Angles)

∠7 + 61° = 180°

∠7  = 180° - 61°

∠7 = 119°

and, ∠5 = ∠7 = 119° (Vertically opposite angle)

and, ∠1 = ∠8 = 61° (Corresponding Angles)

∠1 = 61° and ∠2 is the supplementary angle to given angle

So, ∠1 + ∠2 = 180°

where, supplementary angles are two angles whose measured add up to 180°

61° + ∠2 = 180°

∠2 = 119°

and ∠5 + ∠6 = 180°(Corresponding angle with ∠5)

119°+∠6 = 180°

∠6 = 180 = 119

∠6 = 61°

and, ∠3 = ∠6 = 61° (Corresponding Angle)

∠4 = ∠7 = 119° (Corresponding angle)

Hence, The numbered angle measured is ∠1 = 61°, ∠2= 119, ∠3 = 61, ∠4 = 119, ∠5 = 119, ∠6 = 61 , ∠7 = 119

Learn more about Angles at:

brainly.com/question/1597341

#SPJ1

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