Determine the value of x in this figure, to the nearest degree.

Question

In the diagram E = 65 degrees, D = 55 degrees, C = 115 degrees, the distance between D and C is 52cm. A = 70 degrees, B has a right angle

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Answer 1

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∠EBD=180-(65+55)=60°.

EBD+DBC=EBC=180-EBA=90, ∠DBC=90-60=30°.

∠BDC=180-(30+115)=35°.

Sine Rule:

DC/sinDBC=52/sin30=104=DB/sin115, DB=104sin115=94.256 approx.

Note that sin65=sin115. Also, ∠EDC=90°.

DB/sin65=EB/sin55, EB=DBsin55/sin65=85.192 approx.

EB/x=sin70, x=85.192/sin70=90.659 approx.

Note that x is not an angle but a side. x=91 to the nearest whole number.