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

Answer:

$m\angle IJK=19$°

Step-by-step 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.

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

$10x-13=3x+1+2x+16\\10x-13=5x+17\\10x-5x=17+13\\5x=30\\x=\frac{30}{5}= 6$

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