The required value of k is 9 for the vertical angles 130° and (8k +58).
What is vertically opposite angle?
Angles that are vertically opposite to one another at a certain vertex are formed by two straight lines intersecting. Angles that are vertically opposite to one another are equal.
Given that,
The measurement of one angle ∠a = 130°,
Also, measurement of another angle ∠b = (8k +58)°
Since, both the angles are vertical angles.
Therefore, by vertically opposite angle property, both the angles will be equal.
implies that,
∠a = ∠b
130 = 8k +58
⇒ 130 - 58 = 8k
⇒ 72 = 8k
⇒ k = 9
The value of k for the given angles is 9.
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