Question

I need help with question 19 and 20

Answer 1

Answer:

Question 19.  ∠ JML = 98°

Question 20.  C. Perimeter = 50 units

Step-by-step explanation:

1. Let's solve question 19.

If ∠ JKN = 28 ° and ∠ KLM= 103°, find ∠ JML.

Let's recall that any kite has a pair of congruent angles, in this case ∠ KLM and ∠ KJM are congruents. Thus, ∠ KJM =  103°.

Same as any other quadrilateral, the sum of the measures of the interior angles of a kite is 360°.

Thus, we have:

∠ KLM + ∠ KJM + ∠ JKL + ∠ JML = 360

Replacing with the real values:

103 + 103 + 28 * 2 +  ∠ JML = 360

103 + 103 + 56 +  ∠ JML = 360

 ∠ JML = 360 - 103 - 103 - 56

 ∠ JML = 98°

2. Let's solve question 20.

If JL = 18, NK = 12 and ML = 10.  Let's recall that any kite have two pairs of congruent sides that meet at two different points. In this case, JK and KL are congruents and so do ML and JM.

For finding the value of JK or KL, we use the Pythagorean theorem, this way:

KL²  = NK ² + NL²

KL²  = 12 ² +  9² (NL = 1/2 * JL)

KL²  = 144 + 81

√KL² = √ 225

KL = 15 units

Now, we' re prepared to calculate the perimeter of the kite:

Perimeter = KL + JK + ML + JM (KL and JK are congruents, ML and JM also)

Perimeter = 15 + 15 + 10 + 10

Perimeter = 50 units