Question

Given that m∠IHJ = (2x + 17)° and m∠KHJ = (5x - 10)°, identify m∠IHK .

A.m∠IHK = 70°
B.m∠IHK = 55°
C.m∠IHK = 35°
D.m∠IHK = 25°

Answer 1

HINT: Note that:\[\sin(\angle IHJ)=\frac{IJ}{HJ}\]and:\[\sin(\angle KHJ)=\frac{JK}{HJ}=\frac{IJ}{HJ}\text{ (because JK=IJ in the diagram)}\]You can therefore conclude that:\[\angle IHJ=\angle KHJ\]\[\therefore 2x+17=5x-10\]Solve this to find \(x\) and then use that to calculate \(\angle IHK\)