Answer:
b = 17
∠QPS = 124°
∠SPT = 17°
∠TPR = 39°
Step-by-step explanation:
- The sum of the three angles shown is a linear angle, with a measure of 180°.
This fact can be used to write an equation:
(8b -12)° +b° +(2b+5)° = 180°
11b -7 = 180
11b = 187
b = 17
8b -12 = 8(17) -12 = 124
2b +5 = 2(17) +5 = 39
The value of b is 17.
The angle measures are ...
∠QPS = 124°
∠SPT = 17°
∠TPR = 39°
Answer:
m∠A = 91°
m∠B = 146°
m∠C = 89°
m∠D = 34°
Step-by-step explanation:
- If the four vertices of a quadrilateral lie on the edge of a circle, then this quadrilateral is called cyclic quadrilateral
- In the cyclic quadrilateral each two opposite angles are supplementary (means the sum of their measures is 180°)
- The sum of the measures of the interior angles of any quadrilateral is 360°
In quadrilateral ABCD
∵ A, B, C, And D lie on the circumference of the circle
∴ ABCD is a cyclic quadrilateral
∴ The sum of the measures of each opposite angles is 180°
∵ ∠A and ∠C are opposite angle in the cyclic quadrilateral ABCD
∴ m∠A + m∠C = 180°
∵ m∠A = (2x + 3)°
∵ m∠C = (2x + 1)°
- Add them and equate the answer by 180
∴ (2x + 3) + (2x + 1) = 180
- Add the like terms in the left hand side
∴ 4x + 4 = 180
- Subtract 4 from both sides
∴ 4x = 176
- Divide both sides by 4
∴ x = 44
Substitute the value of x in the expressions of angle A, C, D
∵ m∠A = 2(44) + 3 = 88 + 3
∴ m∠A = 91°
∵ m∠C = 2(44) + 1 = 88 + 1
∴ m∠C = 89°
∵ m∠D = x - 10
∴ m∠D = 44 - 10
∴ m∠D = 34°
- ∠B and ∠D are opposite angles in the cyclic quadrilateral ABCD
∴ m∠B + m∠D = 180°
∴ m∠B + 34 = 180
- Subtract 34 from both sides
∴ m∠B = 146°
1680/61c2 Step-by-step explanation:
Answer:
Cavalier's principle can be used to find the volume of any solid.
Step-by-step explanation:
Cavalier's Principle:
- Cavalier introduced parallel planes and area to describe the relationship between solids.
- Cavalier stated if two solids have the same height and equal areas of the base everywhere along the height then the solids have the same volume.
- Suppose two regions are included between two parallel planes.
- If every plane parallel to these two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes.
- The formula for the volume of a prism is the area of the base times the height.
Answer:
Triangular Prism Calculator
Step-by-step explanation:
