Question

In the diagram below AD||EH I=54 and FBC=44. find CGH

Answer 1

Given,

angle I = 54 degrees

angle FBC = 44 degrees

Recall, the sum of the angles in a triangle is 180 degrees. This means that for triangle BIC,

angle B + angle I + angle BCI = 180 degrees

54 + 44 + angle BCI = 180

angle BCI + 98 = 180

angle BCI = 180 - 98 = 82(sum of angles in a triangle)

Since lines AD and EH are parallel,

angle BCI and angle FGI are corresponding angles(They have similar positions and lie on the same side of the transversal, CI)

Thus,

angle FGI = 82(corresponding angles)

angle CGH and angle

angle CGH and angle FGI are vertically opposite angles. Vertically opposite angles are equal. Thus,

angle CGH = 82 degrees

The reason is 'vertically opposite angles'