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
6x
Step-by-step explanation:
1.2(4x-1)=8x-2=6x
Answer:
2 11/12 cups of flour
Step-by-step explanation:
2 recipes are 2 1/2 cups of flour
1/3 is 1/3 x 1 1/4= 1/3 + 1/12= 5/12
So, 2 11/12 cups of flour
Answer:
<h2>81.28</h2>
Step-by-step explanation:
To solve this kind of problem, we must remember that the word "of" means multiplication in math language, and all percentages numbers can be expressed as a fraction where the denominator is 100. Applying all this, we have
Therefore, all those percentages of 8128 results in 81.28
