The largest angle of a triangle is equal to the sum of the other two angles. The smallest angle is 1/6 of the largest angle. Find the angles of the triangle.
Answers
Answer:
Let the largest angle of a triangle be A and the two smallest angel be B° and C°. If the measure of the largest angle is equal to the sum of other two angle . Then the largest angel= 180°/2 = 90°. The smallest angle is 7/15 of the largest Angle.
Step-by-step explanation:
Step-by-step explanation:
Given :-
The largest angle of a triangle is equal to the sum of the other two angles. The smallest angle is 1/6 of the largest angle.
To find:-
Find the angles of the triangle?
Solution:-
Let the largest angle of a triangle be X°
The smallest angle = 1/6 of the largest angle.
=> (1/6)×X°
=> (X/6)°
Let the third angle be Y°
Given that :
The largest angle of a triangle is equal to the sum of the other two angles.
=> X° = (X/6)°+Y°
=> Y° = X° - (X/6)°
=>Y° = (6X°-X°)/6
=> Y° = 5X°/6
The third angle = 5X°/6
We have ,
The third angles are X°, X°/6 , 5X°/6
We know that
The sum of the three angles in a triangle is 180°
=> X°+(X°/6)+(5X°/6) = 180°
=> (6X°+X°+5X°)/6 = 180°
=> 12X°/6 = 180°
=> 2X° = 180°
=> X° = 180°/2
=> X° = 90°
The largest angle = 90°
The smallest angle = X°/6 = 90°/6 = 15°
Third angle = 5X°/6 = 5(90°)/6 = 5×15° = 75°
Answer:-
The three angles of the given triangle are 90°,15° and 75°
Check:-
The largest angle = 90°
The smallest angle = 90°/6 = 15°
The sum of the third and smallest angle
=> 15°+75°
=> 90°
=> Largest angle
Verified the given relations in the given problem
Used formulae:-
Angle Sum Property:-
The sum of the three angles in a triangle is 180°