Question

100 points if you can figure out all 3 of these math problems

Answer 1

Q1.

KNP = 53°

LNK = 37°

JNL = 143°

JNP = 127°

Q2.

x = 4°

Angle Q = 19°

Angle R = 71°

Q3.

Angle V = 154°

Angle W = 26°

Explanation:

Q1

Angle JNM = Angle KNL

(Vertically opposite angles)

Angle KNL + Angle KNP = 90

(Complementary angles)

7x + 2 + 10x + 3 = 90

17x = 85

x = 5

KNP = 10(5)+3 = 53°

LNK = 7(5)+2 = 37°

JNL = 180-37 = 143°

JNP = 90+37 = 127°

Q2

31 - 3x + 19x - 5 = 90

16x = 64

x = 4°

31-3(4) = 19°

19(4)-5 = 71°

Q3.

V + W = 180

V = 6W - 2

6W - 2 + W = 180

7W = 182

W = 26°

V = 6(26)-2 = 154°

Answer 2

• Answer ⇢1

Given

⇢m∠JNM = (7x+2)°

⇢m∠KNP = (10x + 3)°

⇢m∠LNP = 90°

⇢m∠PNM = 90°

To find

⇢m∠ KNP

⇢m∠ LNK

⇢m∠ JNL

⇢m∠ JNP

Solution

In line KJ,

m∠ KNP + m∠ JNM + m∠PNM = 180°

• The measure of a straight line angle is 180°

putting the values given in the above equation,

⇢(10x + 3)° + (7x+2)° + 90° = 180°

⇢(10x+7x)° + (3+2 +90)° = 180°

⇢17x° + 95° = 180°

⇢17x° = 180°-95°

⇢17x° = 85°

⇢x = (85/17)°

⇢ x = 5°

hence,

⇢m∠ KNP = (10x + 3)° = (10 x 5 +3)° = 53°

⇢m∠ JNP = (7x+2)° + 90° = (7 x 5+2+90)° = 127°

⇢m∠ LNK = 180° - (90+53)° = 37°

⇢m∠ JNL = 180° - 37° = 143°

• Answer ⇢2

Given

⇢m∠Q= (31-3x)°

⇢m∠R= (19x-5)°

⇢m∠Q & ∠R are complementary angles

To find

⇢m∠R

Solution

Given that m∠Q & ∠R are complementary angles,

so ,

m∠Q + ∠R = 90°

• The sum of two complementary angles=90°

putting the values given in the above equation,

⇢(31-3x)° + (19x-5)° = 90°

⇢(19x-3x)° + (31-5)° = 90°

⇢16x° + 26° = 90°

⇢ 16x° = 90° -26°

⇢16x° = 64°

⇢ x = (64/16)°

⇢x = 4

so,

m∠R = (19x-5)° = (19 x 4 -5)° = 71°

• Answer ⇢3

Given

∠V & ∠W are supplementary angles

To find

The measure of ∠V & ∠W

Solution

Given that,

∠V = 6∠W - 2° _______(i)

Also,

∠V + ∠W = 180°_______(ii)

• The sum of two supplementary angles= 180°

putting the value of ∠V in equation (ii)

⇢6∠W - 2° + ∠W = 180°

⇢ 6∠W + ∠W - 2° = 180°

⇢7∠W -2° = 180°

⇢7 ∠W = 180°+ 2°

⇢7 ∠W = 182°

⇢ ∠W = 182°/7

⇢ ∠W = 26°

and

the value of ∠V

⇢= 180° -26°

⇢= 154°

hence , the value of ∠V = 154° & ∠W = 26°