Question

find the measures of the angles of a triangle in each of the following. ​

Answer 1

Answer:

i) One of the angles of a triangle in 130° and the other two angles are equal.

ii) If all the angles are equal then the angle of the triangle is 60° .  

iii) If one of the acute angles of the right triangle is 75°.

Some possibilities are= 50°, 55°

45° , 60°

iv) If the angle is in the ratio 3:5: 10, then the angles of the triangle are 30°, 50°, and 100°.

Step-by-step explanation:

i) One of the angles of a triangle in 130° and the other two angles are equal

If the two equal angles are x, and the sum of angles of a triangle is 180°.

130° + x + x = 180°

2x = 180 - 130

2x = 50

x = 50/2

x = 25 °  

So, the remaining angles are 25 °  , 25 °  .

ii) All the angles are equal.

The sum of angles of a triangle is 180°.

x + x + x = 180°

3x = 180

x = 180/3

x =60 °  

So, angle of triangle is 60° .

iii) One of the acute angles of right triangle is 75°. Find the other acute angle.

The sum of angles of a triangle is 180°.

Sum angles of remaining two angles + 75 = 180°

Sum angles of remaining two angles = 180 -75

Sum angles of remaining two angles = 105°

So, some possibilities are= 50°, 55°

45° , 60°

 

iv) The angle is in the ratio 3:5: 10

If the common multiple is x

then angles are 3x, 5x and 10x

The sum of angles of a triangle is 180°.

3x + 5x + 10x = 180°

18x = 180°

x = 10°

So, the angles of the triangle are 30°, 50°, and 100°.