Question

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

Answer 1

`m\angle IJK=19`°

Explanation:

The triangle for the given scenario is drawn below.

From the triangle
`\Delta IJK`,

`m\angle JKL =10x-13` is an exterior angle for the triangle.

`m\angle IJK=3x+1,m\angle KIJ=2x+16`

Now, according to exterior angle theorem,

Exterior angle is equal to the sum of opposite interior angles.

∴
`m\angle JKL=m\angle IJK+m\angle KIJ`

`10x-13=3x+1+2x+16\\10x-13=5x+17\\10x-5x=17+13\\5x=30\\x=(30)/(5)= 6`

Therefore, the measure of angle IJK is,
`m\angle IJK=3x+1=(3* 6)+1=18+1=19`°.