Answer:
Step-by-step explanation:
Given: quadrilateral ABCD inscribed in a circle
To Prove:
1. ∠A and ∠C are supplementary.
2. ∠B and ∠D are supplementary.
Construction : Join AC and BD.
Proof: As, angle in same segment of circle are equal.Considering AB, BC, CD and DA as Segments, which are inside the circle,
∠1=∠2-----(1)
∠3=∠4-----(2)
∠5=∠6-------(3)
∠7=∠8------(4)
Also, sum of angles of quadrilateral is 360°.
⇒∠A+∠B+∠C+∠D=360°
→→∠1+∠2+∠3+∠4+∠5+∠6+∠7+∠8=360°→→→using 1,2,3,and 4
→→→2∠1+2∠4+2∠6+2∠8=360°
→→→→2( ∠1 +∠6) +2(∠4+∠8)=360°⇒Dividing both sides by 2,
→→→∠B + ∠D=180°as, ∠1 +∠6=∠B , ∠4+∠8=∠B------(A)
As, ∠A+∠B+∠C+∠D=360°
∠A+∠C+180°=360°
∠A+∠C=360°-180°------Using A
∠A+∠C=180°
Hence proved.
credit: someone else
Answer:
Either x = 3, y = 2
or
(3,2) is your answer.
Step-by-step explanation:
2x +y = 8 (1)
y = - x+ 5 (2)
Put equation (2) into equation (1). Use the y value in (2) to go into the y value in (1).
2x - x+5 = 8 Combine the x values
x + 5 = 8 Subtract 5 from both sides
x + 5-5 = 8-5
x=3
Now go back to (2). Put x in for the value of -x. Watch the sign.
y = -3+ 5
y = 2
So the answer is (3,2)
Answer:
Step-by-step explanation:
OFFER A is cheaper.
Step-by-step explanation:
Given,
OFFER A
Pack of 5
£2.75
Pay for 3 packs get 1 free
And
OFFER A
Pack of 5
£2.75
Pay for 3 packs get 1 free
To find which offer is cheaper.
<u>For OFFER A</u>
For 4 Packets he needs to pay £2.75
He needs to buy 40 batteries.
He needs to buy 40÷(4×5) = 2 packets.
Total cost = £2.75
×2 = £5.5
<u>For OFFER B</u>
For 4 Packets he needs to pay £2.52
He needs to buy 40 batteries.
He needs to buy 10 packets.
After discount he has to pay = £2.52
-(£2.52
×
) = £1.68
Total cost = £1.68×10 = £16.8
Hence,
OFFER A is cheaper.
