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For questions 10 – 11, if l ||m, find the values of x and y

iogann1982 [59]

Answer:

10). x = 16

y = 10

11). x = 24

y = 19

Step-by-step explanation:

10). Since l ║ m and a line is transverse intersecting these parallel lines at two distinct points.

Two angles having measures (8x - 14)° and (5x + 34)°are the alternate exterior angles.

Since alternate interior angles are equal in measures.

Therefore, (8x - 14) = (5x + 34)

8x - 5x = 34 + 14

3x = 48

x = 16

Measure of angle (8x - 14)° = 8×16 - 14

= 128 - 14

= 114°

Sum of supplementary angles = 180°

Therefore, (8x - 14)° + (5y + 16) = 180°

114° + (5y + 16)°= 180°

5y = 180 - 130

y = 10

Therefore, x = 16 and y = 10

11). m∠BAC = (5y - 23)°

m∠ACB = 47°

m∠ABC = (2x + 13)°

Since these angles are the angles of a triangle,

(5y - 23)° + 47° + (2x + 13)° = 180°

5y + 2x = 180 - 37

2x + 5y = 143 ------(1)

Lines l ║ m and AC is a transverse,

3x = 5y - 23 [Exterior corresponding angles]

3x - 5y = -23 -----(2)

By adding equation (1) and (2)

(2x + 5y) + (3x - 5y) = 143 - 23

5x = 120

x = 24

From equation (1),

2(24) + 5y = 143

5y = 143 - 48

5y = 95

y = 19

Therefore, x = 24 and y = 19

4 0

3 years ago

Find the central angle of a sector of a circle of the area of the sector and the area of the circle are in the proportion of 3:5

abruzzese [7]

Answer:

$\theta = 216$

Step-by-step explanation:

Given

Area of Sector : Area of Circle = 3 : 5

Required

Determine the central angle

The question implies that

$\frac{Area_{sector}}{Area_{circle}} = \frac{3}{5}$

Multiply both sides by 5

$5 * \frac{Area_{sector}}{Area_{circle}} = \frac{3}{5} * 5$

$5 * \frac{Area_{sector}}{Area_{circle}} = 3$

Multiply both sides by Area{circle}

$5 * \frac{Area_{sector}}{Area_{circle}} * Area_{circle} = 3 * Area_{circle}$

$5 * {Area_{sector} = 3 * Area_{circle}$

Substitute the areas of sector and circle with their respective formulas;

$Area_{sector} =\frac{\theta}{360} * \pi r^2$

$Area_{circle} = \pi r^2$

So, we have

$5 * \frac{\theta}{360} * \pi r^2 = 3 * \pi r^2$

Divide both sides by $\pi r^2$

$5 * \frac{\theta}{360} * \frac{ \pi r^2}{\pi r^2} = 3 * \frac{\pi r^2}{\pi r^2}$

$5 * \frac{\theta}{360} = 3$

Multiply both sides by 360

$360 * 5 * \frac{\theta}{360} = 3 * 360$

$5 * \theta = 3 * 360$

Divide both sides by 5

$\frac{5 * \theta}{5} = \frac{3 * 360}{5}$

$\theta = \frac{3 * 360}{5}$

$\theta = \frac{1080}{5}$

$\theta = 216$

Hence, the central angle is 216 degrees

3 0

2 years ago

Define the variables for the situation. Then enter an equation.

stepan [7]

Answer:

A= L + 5

Step-by-step explanation:

Andrews class is equal to Lauren's class and there are more 5 students

4 0

3 years ago

Oscar painted1/6 of a wall in 2/3hours at this rate how many hours will it take him to paint the whole wall?

topjm [15]

Answer:

b

Step-by-step explanation:

the answer is b because you add all those together then boom

8 0

3 years ago

Find the value of x I’d appreciate if you could explain as well if not that’s fine

Kipish [7]

All the angles in a circle equal to 360 degrees. So basically just add up all the known values: 23+23+15=61 and then subtract that from 360: 360-61=299.

You can also do 23+23+15+x=360. Adding it all becomes 61+x=360, subtract 61 from both sides of the equation, and you get x=299.

(Something to help remember is that the angle is obtuse, meaning it’s automatically more than 90 degrees, hope this helps!)

7 0

2 years ago