Question

the three angles of a triangle are in the ratio 2 : 1 : 2: find the measure of the angles and state the kind of triangle​

Answer 1

Answer:

32°

16°

32°

Kind of Triangle:

by side: isosceles triangle

by angle: acute angled triangle.

Step-by-step explanation:

let one part (constant) be x

ratio of the angles of triangle = 2:1:2

(angle sum property of triangles states that the summ of all the angles of a triangle is 180°)

:. 2x + x + 2x = 180°

=> 5x = 180°

=> x = 180°/5

=> x = 16°

therefore

angle 1 = 2x = 2×16 = 32°

angle 2 = x = 16°

angle 3 = 2x = 32°

kind of triangle:

by angle: ACUTE ANGLED TRIANGLE (as all the angles of the given triangle are less than 90° it is an acute angled triangle)

by side: ISOSCELES TRIANGLE (as one of the property of an isosceles triangle is that the side opposite to the equal angles are equal)

Answer 2

Step-by-step explanation:

Let the angle= x

each angle = 2x, x, 2x

According to angle sum property of a triangle,

2x + x + 2x = 180°

5x = 180°

x = 180°/5

x = 36°

angles of the triangle are:

36° , 72° ,72°

it is an acute triangle.