By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3
Step-by-step explanation:
The supplementary angles are:
- Two angles their sum is 180°
- The supplement of an acute angle is an obtuse angle and vice versa
- The supplement of a right angle is a right angle
- If one angle is supplement to two other angles, then the two angles are equal in measure (if 50° is supplement to angles X and Y, then X and y must be 130°)
- Supplement angles of congruent angles are congruent (If angles X and Y are supplement to angles A , B and angles A , B are congruent, then angles X and Y are congruent
∵ ∠1 and ∠2 are supplementary
∴ m∠1 + m∠2 = 180° ⇒ (1)
∵ ∠3 and ∠4 are supplementary
∴ m∠3 + m∠4 = 180° ⇒ (2)
We can equate the left hand sides of (1) and (2) because the right hand sides are equal
∴ m∠1 + m∠2 = m∠3 + m∠4 ⇒ (3)
∵ ∠1 ≅ ∠4
∴ m∠1 = m∠4
- Substitute m∠4 by m∠1 in (3)
∴ m∠1 + m∠2 = m∠3 + m∠1
- Subtract m∠1 from both sides
∴ m∠2 = m∠3
∴ ∠2 ≅ ∠3
By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3
Learn more:
You can learn more about supplementary angles in brainly.com/question/10483199
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I removed all eight corners, leaving the total area unchanged.
I removed the central cube of the top surface obtaining an increase of the surface area with four units.
I removed one cube from the middle of an edge at the top (any of the four remaining) and I arrived at a figure with ten cubes less then the original one but with the same surface area.
https://nrich.maths.org/787/solution
Answer:
59)
Therefore the height of the pyramid is 14 meter.
60)
Therefore the Diameter of Cone is 17.32 cm.
Step-by-step explanation:
59 )
Given:
Shape is Rectangular Pyramid,
Length = 3 meter
Width = 8 meter
Volume of Rectangular Pyramid = 112 cubic meter
To Find:
Height:
Solution:
We Know,
Substituting the given values we have
Therefore the height of the pyramid is 14 meter.
60 )
Thee shape is of Cone
Given:
Height= 5 cm
Volume of cone = 125 π cm³
To Find:
Diameter of a cone = d = ?
Solution:
We know,
Substituting the given values we have
Therefore the Diameter of Cone is 17.32 cm.
Answer:
second one
112 red tomatoes
Step-by-step explanation:
8 - 5 = 3
42/3 = 14
14 times 8 = 112
