76.8k views
3 votes
100 points if you can figure out all 3 of these math problems

100 points if you can figure out all 3 of these math problems-example-1
User Grafix
by
8.4k points

2 Answers

5 votes

Answer:

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°

User BenMills
by
7.6k points
4 votes
  • 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°

User Hukam
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories