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3 years ago

................. help please

Mathematics

2 answers:

Alexeev081 [22]3 years ago

8 0

Answer:

Step-by-step explanation:

Angle (2x + 15) degrees and 135 degrees lie on a straight line. The sum of the angles on a straight line is 180 degrees. It means that

2x + 15 + 135 = 180

2x + 150 = 180

Subtracting 150 from the left hand side and the right hand side of the equation, it becomes

2x + 150 - 150 = 180 - 150

2x = 30

Dividing the left hand side and the right hand side of the equation by 2, it becomes

2x/2 = 30/2

x = 15

Therefore,

Angle (2x + 15) = 2 × 15 + 15

= 30 + 15 = 45 degrees

Since Line m is parallel to line n, then angle (2x + 15) and angle 1 are alternate angles. Alternate angles are equal. Therefore

Angle 1 = 45 degrees

egoroff_w [7]3 years ago

6 0

Answer:

x = 15

m∠1 = 45°

Step-by-step explanation:

2x + 15 + 135 = 180

2x = 180 - 15 - 135

2x = 30

x = 30/2

x = 15

180 - 135 = 45°

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The answers of the given geometrical shapes are:

1. 226.29 cubic yard

2. 46.1 cubic inches

3. 2413.71 cubic inches

4. 234.67 cubic millimeter

5. 340.48 cubic yards

6. 113.14 cubic feet

7. 528 cubic centimeter

8. 905.14 cubic centimeter

9. 56.57 cubic feet

<h3>what is mensuration?</h3>

Mensuration is the branch of geometry that deals with measurement of volumes and areas of geometrical shapes.

Analysis:

1. volume of cylinder =π $r^{2}$ h. where r = 6/2 = 3 yard, h = 8 yard

= $\frac{22}{7}$ x $3^{2}$ x 8 = 226.29 cubic yard

2. volume of cone = $\frac{1}{3}$ x π $r^{2}$ h. where r = 2inches, h = 11

= $\frac{1}{3}$ x $2^{2}$ x $\frac{22}{7}$ x 11 = 46.1 cubic inches

3. volume of cylinder = π $r^{2}$ h. where r = 8, h = 12

= $\frac{22}{7}$ x $8^{2}$ x 12 = 2413.71 cubic inches

4. volume of cone = $\frac{1}{3}$ x π $r^{2}$ h. where r = 4, h = 14

= $\frac{1}{3}$ x $\frac{22}{7}$ x $4^{2}$ x 14 = 234.67 cubic millimeter

5. volume of cone = $\frac{1}{3}$ x π $r^{2}$ h. where r = 5, h = 13

= $\frac{1}{3}$ x $\frac{22}{7}$ x $5^{2}$ x 13 = 340.48 cubic yards

6. volume of cylinder = π $r^{2}$ h. where r = 3, h = 4

= $\frac{22}{7}$ x $3^{2}$ x 4 = 113.14 cubic feet

7. volume of cone = $\frac{1}{3}$ x π $r^{2}$ h. r = 6, h = 14

= $\frac{1}{3}$ x $\frac{22}{7}$ x $6^{2}$ x 14 = 528 cubic centimeter

8. volume of cylinder = π $r^{2}$ h. where r = 6, h = 8

= $\frac{22}{7}$ x $6^{2}$ x 8 = 905.14 cubic centimeter

9. volume of cylinder = π $r^{2}$ h. where r = 1.5, h = 4

= $\frac{22}{7}$ x $1.5^{2}$ x 4 = 56.57 cubic feet

In conclusion, the volume of cylinders and cones for the given dimensions are:

1. 226.29 cubic yard

2. 46.1 cubic inches

3. 2413.71 cubic inches

4. 234.67 cubic millimeter

5. 340.48 cubic yards

6. 113.14 cubic feet

7. 528 cubic centimeter

8. 905.14 cubic centimeter

9. 56.57 cubic feet

Learn more about mensuration: brainly.com/question/18541562

#SPJ1

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