Question

2 Classify each triangle by its angles and its sides.

Answer 1

10) acute triangle

13) right triangle

Explanation:

all triangles have angles that add up to 180 degrees

find the third angle of the triangle by subtracting the known angles from 180

180-75-78=27

acute triangles have no angles that surpass 90 degrees which fits that triangle's description

180-54-36=90

since one angle is 90 degrees, it is a right triangle

Answer 2

`\huge\boxed{\bf\:10) \: Acute \: angled \: triangle}`

`\huge\boxed{\bf\:11) \: Right \: angled \: triangle}`

Explanation:

▪︎ Question 10 :

We need to find the missing angle at first. Take it as 'x' .

We know through the angle sum property of a triangle that the total sum of all the angles in a triangle will sum up to 180°. Hence,

75° + 78° + x° = 180°

153° + x° = 180°

x° = 180° - 153°

x° = 27°

Then, since all the angles are less than 90°, we can say that the triangle is an acute angled triangle.

`\rule{150pt}{2pt}`

▪︎ Question 11 :

Just like the above question, we need to find the missing angle at first. Take it as 'y' .

The total sum of all the angles in a triangle will sum up to 180° (angle sum property of triangles). Hence,

36° + 54° + y° = 180°

90° + y° = 180°

y° = 180° - 90°

y° = 90°

Since, one angle is equal to 90°, the given triangle is a right angled triangle.

`\rule{150pt}{2pt}`