In AIJK, IK is extended through point K to point L, m_JKL =(10x – 13), mZIJK = (3x + 1)', and mZKIJ = (2x + 16)º.Find mZIJK
Accepted Solution
A:
Answer:[tex]m\angle IJK=19[/tex]°Step-by-step explanation:The triangle for the given scenario is drawn below.From the triangle [tex]\Delta IJK[/tex],[tex]m\angle JKL =10x-13[/tex] is an exterior angle for the triangle.[tex]m\angle IJK=3x+1,m\angle KIJ=2x+16[/tex]Now, according to exterior angle theorem, Exterior angle is equal to the sum of opposite interior angles.∴ [tex]m\angle JKL=m\angle IJK+m\angle KIJ[/tex][tex]10x-13=3x+1+2x+16\\10x-13=5x+17\\10x-5x=17+13\\5x=30\\x=\frac{30}{5}= 6[/tex]Therefore, the measure of angle IJK is, [tex]m\angle IJK=3x+1=(3\times 6)+1=18+1=19[/tex]°.