the sum of the measure of two angles is 100°and their diffrence is 2π/9 radian ,find the measure of angle in radian????
Answers
Answer:
A+B = 100°
180° = pi
100° = (pi×100)/180° = 5pi/9
A+B = 5pi/9
A-B = 2pi/9
Add both the equations
2A = 7pi/9
A = 7pi/18
Similarly, B=3pi/18
Given :-
The sum of the measure of two angles is 100°
The difference of the measure of the two angles is 2π/9©
To find :-
The measure of each angle in radians.
Solution :-
Let the two angles be X° and Y°
The sum of two angles = 100°
X+Y = 100° --------------(1)
Their difference = 2π/9©
We know that
π© = 180°
=> 2π/9© = 2×180°/9 = 40°
Therefore, X-Y = 40° ---------(2)
From (1)&(2)
X+Y = 100°
X-Y = 40°
(+)
_________
2X+0 = 140°
_________
=> 2X = 140°
=> X = 140°/2
=> X = 70°
On substituting the value of X in (1) then
70°+Y = 100°
=> Y = 100°-70°
=> Y = 30°
We have,
X= 70° = 70×π/180©
=>X = 70π/180©
=> X = 7π/18©
and
Y = 30°
=> Y = 30×π/180©
=> Y = π/6©
Therefore, The angles are 7π/18© and
7π/18© and π/6©
Answer :-
The measure of each angles are 7π/18© and
π/6©
Used formulae:-
→ π© = 180°