Question

19. Given that angle BFC = 58°. Angle BXG = 48° and angle CBF 22 Find () 2BGX (iv) BCG (i) 2BGF (iv) ZBFG (ii) BCF H EE 58 48° D C 220 A- Figure 5.74​

Answer 1

The unknown angles in the cyclic quadrilateral is as follows:

∠BGX = 74° (sum of angles in a triangle)

∠BGF = 180° (opposite angles of cyclic quadrilateral are supplementary)

∠BCF = 100°(sum of angles in a triangle)

∠BCG  = 26°

∠BFG = 22°

Cyclic Quadrilateral

A cyclic quadrilateral has all its angles equal to 360 degrees. The sum of angles in a cyclic quadrilateral is equals to 360 degrees.

Let's find the missing angles as follows:

∠BGX = 180 - 48 - 58 = 74° (sum of angles in a triangle)

∠BGF = 180 - 100 = 80° (opposite angles of cyclic quadrilateral are supplementary)

∠BCF = 180 - 22 - 58 = 100°(sum of angles in a triangle)

∠BCG = 100 - 74 = 26°

∠BFG ≅ CBF = 22°(alternate angles)

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