Question

NO LINKS!!
Please help me with #18, 19, & 20

Answer 1

• 18) 30°,
• 19) 38,
• 20) 41.34.

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Since P is incenter, we have properties of incenter applicable to given questions:

• P is the intersection of angle bisectors;
• P is equidistant from the sides of the triangle.

Question 18

Since JN is angle bisector of ∠J, set up equation:

• 7x - 6 = 5x + 4
• 7x - 5x = 4 + 6
• 2x = 10
• x = 6

Angle measures of the triangle are:

• m∠J = 2 (5*6 + 4) = 3(34) = 68
• m∠L = 2(26) = 52

Then, according to triangle sum:

• m∠K = 180 - (68 + 52) = 180 - 120 = 60

Then, find the missing angle:

• m∠JKP = 60/2 = 30

Question 19

Sides are equidistant from incenter:

• PN = PM = PO

Set up equation and solve or x:

• 9x - 34 = 3x + 14
• 9x - 3x = 14 + 34
• 6x = 48
• x = 8

Find one of equal segments:

• PN = 3*8 + 14 = 24 + 14 = 38

Hence, MP = 38

Question 20

ΔMPJ and ΔOPJ are congruent right triangles as MP = OP and JP is common hypotenuse, therefore JM and JO are congruent as corresponding sides:

• 2x + 3 = 5x - 45
• 5x - 2x = 3 + 45
• 3x = 48
• x = 16

Then JM is:

• JM = 2*16 + 3 = 32 + 3 = 35

We know MP = NP = 22.

Find JP using Pythagorean:

• JP =
  `JP = √(35^2+22^2)=√(1709) =41.34`