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
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