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# In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG and FH are ...

### Question

In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG and FH are chords. If < FHG = 424$$^{\circ}$$ and < EFH = 34$$^{\circ}$$

### Options

A) 34$$^{\circ}$$

B) 42$$^{\circ}$$

C) 52$$^{\circ}$$

D) 76$$^{\circ}$$

### Explanation:

< EFH = < EGH = 34$$^{\circ}$$ (angles n the same segment)

< GHF = < GEF = 42$$^{\circ}$$(angles in the same segment)

< FOG = 42 + 34 = 76(exterior angle)

< FOG = < EOH = 76(vertically opposite angle)

< EDO = 90$$^{\circ}$$, < DOE = $$\frac{76}{2}$$ = 38$$^{\circ}$$

< HEG = 90$$^{\circ}$$ - 38$$^{\circ}$$ = 52$$^{\circ}$$

## Dicussion (1)

• < EFH = < EGH = 34$$^{\circ}$$ (angles n the same segment)

< GHF = < GEF = 42$$^{\circ}$$(angles in the same segment)

< FOG = 42 + 34 = 76(exterior angle)

< FOG = < EOH = 76(vertically opposite angle)

< EDO = 90$$^{\circ}$$, < DOE = $$\frac{76}{2}$$ = 38$$^{\circ}$$

< HEG = 90$$^{\circ}$$ - 38$$^{\circ}$$ = 52$$^{\circ}$$