Three straight lines EF, GH and LK interest at O as shown above. If ∠KOF = \(52^\circ\) and ∠LOH = \(85^\circ\), calculate the size of ∠EOG.
Question 1 Report
Three straight lines EF, GH and LK interest at O as shown above. If ∠KOF = \(52^\circ\) and ∠LOH = \(85^\circ\), calculate the size of ∠EOG.
Answer Details
To find the size of ∠EOG, we need to use the fact that the sum of the angles around point O is 360 degrees.
So, we can start by finding the size of ∠FOG and ∠EOH, which are vertical angles to ∠KOF and ∠LOH respectively:
∠FOG = ∠KOF = 52∘
∠EOH = ∠LOH = 85∘
Now, we can use the fact that opposite angles in a parallelogram are equal to find the size of ∠EOG. Since EF is parallel to HG, we have:
∠EOG = 180 - ∠FOG - ∠EOH
Substituting the values we found earlier, we get:
∠EOG = 180 - 52 - 85
∠EOG = 43 degrees
Therefore, the size of ∠EOG is 43 degrees.
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