Help!! What is arc HLK? Thankyou!

We know Angle HMK is half the sum of Arc JI and Arc HLK. So, we can set up an equation.

8x - 1 = 1/2 (3x + 2 + 15x - 36)

8x - 1 = 1/2 (18x - 34)

16x - 2 = 18x - 34

32 = 2x

16 = x

Then, we can substitute x into Arc HLK

HLK = 15x - 36

HLK = 240 - 36

Arc HLK = 204°

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is