Only Question #5!
If JKLM is a rectangle, find
Measure NML

Answer;

5. 22°

6. 74°

Step-by-step explanation:

5. Since rectangle JKLM has two equal diagonals that intersect each other, therefore JN = MN.

If JN = MN therefore:

m<NMJ = m<NJM

Thus:

3x + 38 = 7x - 2

Solve for x. Collect like terms

3x - 7x = -38 - 2

-4x = - 40

Divide both sides by -4

x = 10

✔️Find m<NMJ

m<NMJ = 7x - 2

Plug in the value of x

m<NMJ = 7(10) - 2 = 70 - 2

m<NMJ = 68°

✔️Find m<NML;

m<NML = 90 - 68° (Complimentary angles)

m<NML = 22°

6. Diagonal of a rhombus bisects teach vertex angle, this means that <U is divided into two equal parts. Therefore:

10x - 23 = 3x + 19

Solve for x. Collect like terms

10x - 3x = 23 + 19

7x = 42

Divide both sides by 7

x = 6

✔️Find m<RST:

m<SUT = m<RST (opposite angles of a rhombus are congruent)

Thus,

m<SUT = (10x - 23) + (3x + 19)

Plug in the value of x

m<SUT = (10(6) - 23) + (3(6) + 19)

= (60 - 23) + (18 + 19)

= 37 + 37

m<SUT = 74°

Also, m<RST = 74°

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