( a ) If an angle is half of its complementary angle, then find its degree measure.
( b ) The two complementary angles are in the ratio 1 : 5. Find the measures of the angles
( c ) If an angle is 14° more than its complement, then find its measure.
( d ) Is it possible to construct triangles with its three angles being 37°, 80° and 95°?
Give reason for your answer.
( e ) If the angles of a triangle are in the ratio 5 : 3: 2 then what is the shape of the triangle ?
Answers
( a ) If an angle is half of its complementary angle, then find its degree measure.
Two angles are complementary if their sum is equal to 90 degrees. The angle is 30 degrees.
( b ) The two complementary angles are in the ratio 1 : 5. Find the measures of the angles?
Two complementary angles are in the ratio = 1 : 5
Let these angles be x and 5x
∴ x + 5x = 90°
⇒ 6x = 90°
⇒ x = 90°/6 = 15°
∴ Angles will be 15° and 15° × 5 = 75°
( c ) If an angle is 14° more than its complement, then find its measure.
90°
The complement of 14° is the angle that when added to 14° forms a right angle (90° ).
let's begins;
x+x+14=90°
2x + 14 = 90°
2x = 90 -14
2x = 76
x = 76/2 = 38
1st x= 38
2nd number = x + 14 = 38+14 = 52°
( d ) Is it possible to construct triangles with its three angles being 37°, 80° and 95°?
ANSWER : NO
( e ) If the angles of a triangle are in the ratio 5 : 3: 2 then what is the shape of the triangle ?
5x + 3x + 2x = 180 °
10x = 180°
x = 180/10
x = 18°
5x = 5 x 18 = 90°
3x = 3 x 18 = 54°
2x = 18 x 2 = 36 °