Please answer it’s important!

The m∠HIK is 42°

Step-by-step explanation:

When two lines intersected at a point, then they formed pairs of linear anglesLinear angles are supplementary, which means the sum of their measures is 180°

In the given figure

∵ Line HJ intersects line KD at the point I

→ By using the facts above

∴ ∠HIF and ∠HIK formed a pair of linear angles

∴ ∠HIF and ∠HIK are Supplementary

→ That means the sum of their measures is 180°

∴ m∠HIF + m∠HIK = 180°

∵ m∠HIF = 138°

→ Substitute it in the equation above

∴ 138° + m∠HIK = 180°

→ Subtract 138 from both sides

∴ 138° - 138° + m∠HIK = 180° -138°

∴ m∠HIK = 42°

∴ The m∠HIK = 42°

Use sum of arithmetic series:
Sum of n terms = (n/2)(2a + (n - 1)d)
where a is the first term, -6
d is the common diff, 6 - 2 = 4
and n is the number of terms, 20

Sum of first 20 terms
= (20/2)(2(-6) + 19(4))
= 640