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°
