Please answer to these both questions
Answers
Answer:
Given: x + y = w + z
To prove: AOB is a line.
We know that if the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line.
Step-by-step explanation:
From the figure we can see that,
(x + y) + (w + z) = 360° (complete angle)
It is given that (x + y) = (w + z),
Hence (x + y) + (w + z) = 360° can be written as (x + y) + (x + y) = 360°
2x + 2y = 360°
2(x + y) = 360°
x + y = 360°/2 = 180°
Since the sum of adjacent angles, x and y with OA and OB as the non-common arms is 180° we can say that AOB is a line.
Answer:
Step-by-step explanation:
1st
x+y =w +z
x + y + w +z = 360 (Angle of circle)
(x+y) + (x +y )= 360 (Because x+y =w +z)
2 (x +y ) = 360
Therefore x + y = 180
Therefore AOB IS A LINE (BECAUSE ANGLE OF ONE LINE IS 180 DEGREE)
2ND
Let the point of intersection of BC and AD be O
In △ABO
⇒∠B<∠A
Thereore, ⇒AO<BO (1) (side opposite to greater angle is largest)
Similarly,
In △COD
⇒∠C<∠D
Thereore, ⇒DO<CO (2) (side opposite to greater angle is largest)
Adding (1) and (2) we get,
⇒BO+OC>AO+DO
⇒BC>AD
Hence proved.
HOPE THIS HELP!!❤