Difference between measure of major arc and its corresponding minor arc is 40 degree find the measure of both the arcs. Answer it briefly with correct explanation . ( Figure not provided in book from where Question is taken)
Answers
Step-by-step explanation:
Given :-
Difference between measure of major arc and its corresponding minor arc is 40°
To find :-
Find the measure of both the arcs ?
Solution :-
Let the measure of major arc be X°
Let the measure of minor arc be Y°
We know that
The sum of the measurements of the major and minor arcs = 360°
X° + Y° = 360° --------------(1)
Given that
Difference between measure of major arc and its corresponding minor arc in a circle is 40°
=> X° - Y ° = 40° -----------(2)
On adding (1)&(2)
X° + Y° = 360°
X° - Y° = 40°
(+)
____________
2X° + 0 = 400°
____________
=> 2X° = 400°
=> X° = 400°/2
=> X° = 200°
The measure of major arc = 200°
On Substituting the value of X° in (1)
=> 200° + Y° = 360°
=> Y° = 360°-200°
=> Y° = 160°
The measure of minor arc = 160°
Answer:-
The measure of major arc = 200°
The measure of minor arc = 160°
Used formulae:-
- The sum of the measurements of the major and minor arcs in a circle = 360°