The measure of two angles of triangle are in the ratio 5 ratio 3 the measure of third angle is half the difference of measures of above two angles find the measure of each angle
Answers
Here is your answer user.
Answer:
Angles of the given triangle are 100°, 60° and 20°.
Step-by-step explanation:
Given:- Two angles of a triangle are in the ratio 5 : 3.
3rd angle is half the difference of measures of two given angles.
To Find:- Value of each angle of the triangle.
Solution:-
Let the two given angle be 5x and 3x.
∴ 3rd angle = 5x - 3x ÷ 2
As we know, In a triangle sum of all the angle is always 180°.
∴ 5x + 3x + ( (5x - 3x) ÷ 2 ) = 180
⇒ 8x + ( 2x ÷ 2 ) = 180
⇒ 8x + x = 180
⇒ 9x = 180
⇒ x = 180 ÷ 9
⇒ x = 20
∴ First angle = 5x = 5×20
= 100°
Second angle = 3x = 3×20
= 60°
Third angle = ( (5x - 3x) ÷ 2) = 2x ÷ 2
= 20°
Therefore, Angles of the given triangle are 100°, 60° and 20°.
#SPJ3