............................,,,;,,...............:......
Answer:
∠1 ≅ ∠2 ⇒ proved down
Step-by-step explanation:
#12
In the given figure
∵ LJ // WK
∵ LP is a transversal
∵ ∠1 and ∠KWP are corresponding angles
∵ The corresponding angles are equal in measures
∴ m∠1 = m∠KWP
∴ ∠1 ≅ ∠KWP ⇒ (1)
∵ WK // AP
∵ WP is a transversal
∵ ∠KWP and ∠WPA are interior alternate angles
∵ The interior alternate angles are equal in measures
∴ m∠KWP = m∠WPA
∴ ∠KWP ≅ ∠WPA ⇒ (2)
→ From (1) and (2)
∵ ∠1 and ∠WPA are congruent to ∠KWP
∴ ∠1 and ∠WPA are congruent
∴ ∠1 ≅ ∠WPA ⇒ (3)
∵ WP // AG
∵ AP is a transversal
∵ ∠WPA and ∠2 are interior alternate angles
∵ The interior alternate angles are equal in measures
∴ m∠WPA = m∠2
∴ ∠WPA ≅ ∠2 ⇒ (4)
→ From (3) and (4)
∵ ∠1 and ∠2 are congruent to ∠WPA
∴ ∠1 and ∠2 are congruent
∴ ∠1 ≅ ∠2 ⇒ proved
The circumference of the circle is actually the perimeter ( length of the boundary ) of the circle . And a part of the circle which lies between two distinct points on the circumference of the circle is called an arc . If the length of the arc is less than half the circumference , it is called minor arc and remaining portion which is more than half of the circle ( but natural ) is called major arc .
When these two points , which make the arc are joined separately to the centre of circle , these arms make angle at the centre . This is called the angle subtended by the arc at the centre of the circle .
There is a beautiful logical relation exists between arc length and the angle , the arc makes ( subtends ) at the centre of the circle . This relation is as under , the wholle circle subtends an angle of 360 degree at the centre . Half the circumference subtendr 360 / 2 ie 180 degree at the centre . The logical relation becomes Arc Length = Circumference × angle in degrees it ( the arc ) subtends at the centre of the circle / 360 degree . So the answer is very simple :- The Arc Length = 36 × 90 / 360 or 9 units ( may be centimetres or metres or inches , feet , yards , etc ) . Which is definitely length of the minor arc . The length of the major arc ( remaining portion of the circumstance ) is 36 - 9 = 27 units . Hence the required answer of the sum is 9 units .
<h3>
Answer: (-infinity, 7]</h3>
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Explanation:
The first interval (-infinity, 3) describes any number less than 3, so we can write x < 3 in short hand (where x is the unknown number).
The second interval (-1, 7] means we start at -1 and stop at 7. We do not include -1 but include 7. So we say that 
(ie x is between -1 and 7; exclude -1, include 7)
If you were to graph each ona number line, you would see that the too intervals have overlapping parts. The right most edge extends out as far as x = 7. There is no left most edge as it goes onforever that direction.
Therefore, the to intervals combine to get 
which turns into the interval notation answer of (-infinity, 7]
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It might help to think of it like this: x < 3 and say "x is some number that is less than 3, or it is between -1 and 7". So x could be anything less than 7, including 7 itself.
Answer:
a
Step-by-step explanation:
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