Three straight lines EF, GH and LK interest at O as shown above. If ∠KOF = 52∘ ∘ and ∠LOH = 85∘ ∘ , calculate the size of ∠EOG.

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.