1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ad-work [718]
3 years ago
11

12. In ∆PQR, if m∠P is 14 less than five times x, m∠Q is five less than x, and m∠R is nine less than twice x, find x and the mea

sure of each angle. 13. In ∆JKL, if m∠J is seven less than m∠L and m∠K is 21 less than twice m∠L, find the measure of each angle. 14. In ∆BCD, if BC ≅ BD , m∠B = 13x – 35, m∠C = 5x – 19, and m∠D = 2x + 14, find x and the measure of each angle. 15. In ∆WXY, if∠X ≅ ∠Y , WX = 9x – 11, XY = 4x + 1, and WY = 7x – 3, find x and the measure of each side.

Mathematics
1 answer:
pychu [463]3 years ago
3 0

Answer:

12)x=26.125°

∠P  = 115.625°

∠Q =21.125°

∠R=43.25°

13)x=52°

∠L=52°

∠J =45°

∠K =69°

14)x=11°

∠C = 36°

∠D =36°

∠B = 108°

15)x=7

WX = 52

WY=52

XY =29

Step-by-step explanation:

12)In ∆PQR

∠P is 14 less than five times x = 5x-15

∠Q is five less than x=x-5

∠R is nine less than twice x=2x-9

Angle sum property of triangle : The sum of all angles of triangle is 180°

So,5x-15+x-5+2x-9=180

8x-29=180

8x=180+29

x=\frac{180+29}{8}

x=26.125

So,∠P  = 5x-15 =5(26.125)-15=115.625°

∠Q =x-5=26.125-5=21.125°

∠R=2x-9=2(26.125)-9=43.25°

13)  In ∆JKL

Let the angle L be x

∠L=x

∠J is seven less than ∠L=x-7

∠K is 21 less than twice ∠L=2x-21

Angle sum property of triangle : The sum of all angles of triangle is 180°

So, x+x-7+2x-21=180°

4x-28=180°

4x=180+28

x=\frac{180+28}{4}

x=52

∠L=x=52°

∠J =x-7=52-7=45°

∠K =2x-21=2(45)-21=69°

14)In ∆BCD

BC ≅ BD(Given)

Opposite angles of equal sides are equal

So, ∠C =∠D

∠C = 5x – 19

∠D = 2x + 14

So, 5x-19=2x+14

3x=33

x=11

∠C = 5x – 19=5(11)-19=36°

∠D = 2x + 14=2(11)+14=36°

∠B = 13x – 35=13(11)-35=108°

15) In ∆WXY

∠X ≅ ∠Y(Given)

Opposite sides of equal angles are equal

WY=WX

WX = 9x – 11

WY = 7x – 3

So, 9x-11=7x-3

2x=14

x=7

So, WX = 9x – 11=9(7)-11=52

WY=52

XY = 4x + 1=4(7)+1=29

You might be interested in
A triangle has two sides of length 9 and 14 what is the smallest possible whole number length for the third side
melisa1 [442]

Let the third side = x.

The sum of any two sides must be greater than the third side

14 + 9 > x

  23 > x

14 + x > 9

   x > -5

9 + x > 14

   x > 5

So 5 < x < 23

6 0
2 years ago
Brianliest help please
Mamont248 [21]

Answer:

answer is option C

3+7=10

7-3=4

5 0
2 years ago
Read 2 more answers
Solve for p.
Arte-miy333 [17]
2(p+1)=24
divide both sides by two
p+1=12
subtract 1 from both sides
p=11
4 0
3 years ago
Find the function value of cos^2 (7pi/8)
Kamila [148]
\cos^2\dfrac{7\pi}8=\dfrac12\left(1+\cos\dfrac{7\pi}4\right)
=\dfrac12+\dfrac12\cos\left(-\dfrac\pi4\right)
=\dfrac12+\dfrac12\cos\dfrac\pi4
=\dfrac12+\dfrac1{2\sqrt2}
=\dfrac{\sqrt2+1}{2\sqrt2}
=\dfrac{2+\sqrt2}4
7 0
2 years ago
Solve in standard form 2+4i÷7+I
tia_tia [17]


I rewrote it as → L + 2 + \frac{2i}{7}
7 0
3 years ago
Other questions:
  • What is the slope of the line passing through the points (6, 7) and (1, 5) ?
    12·2 answers
  • Ms.Tao flies roundtrip twice yearly between Jacksonville and Los Angeles on business the distance between the two cites is 2,150
    9·1 answer
  • What is the quotient?
    15·2 answers
  • Three consecutive vertices of a parallelogram are points (2, 4), (0, 0), and (6, 0). The fourth vertex is point
    7·1 answer
  • The relationship between sets of rational numbers is pictured below
    13·1 answer
  • the values in the table represent a linear function. what is the common difference of the arithmetic sequence x: 1 2 3 4 5 y: 11
    7·2 answers
  • Morgan works at a store that sells clothing accessories. The supply function
    13·2 answers
  • SOMEONE, PLEASE HELP!!!!!!
    14·2 answers
  • Function f is shown on the graph. What is the range of f?
    13·1 answer
  • What is the curve : y= -2x
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!