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 measure 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.

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=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=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

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

just sum

10 + 10 = 20