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:
56.52 cm³
Step-by-step explanation:
Diameter= 2 ×radius
Radius
= 6 ÷2
= 3cm
Height, h= 6cm
Volume of the cone
= 56.52 cm³
Answer:
Step-by-step explanation:
According to Angles of intersecting chords theorem:
∠GAJ =
Where ∠GAJ = 50 , BD = 24 and GJ = ?
50 =
Multiplying both sides by 2
100 = 24 + GJ
GJ = 100-24
GJ = 76 degrees
Answer:
Part A: L(-1,9) M(-4,3) N (-8,5)
Step-by-step explanation: