Learn How to Find Missing Angles in Triangles

By Team Aakash Byju's | 18th January 2023

Find the value of x in each of the following figures.

55

0

x

C

B

A

P

Q

R

x

120

0

2x

Q

P

R

x

25

0

30

0

The value of x for images (i), (ii) and (iii) are

(i) x = 40° (ii) x = 35° (iii) x = 125°

55

0

x

C

B

A

P

Q

R

x

120

0

2x

Q

P

R

x

25

0

30

0

Consider the first triangle labelled as (i). The exterior angle formed by producing a triangle is equal to the sum of the 2 opposite interior angles.

=> 120° = 2x+x => 120° = 3x => x = 40°

55

0

x

C

B

A

P

Q

R

x

120

0

2x

Q

P

R

x

25

0

30

0

In image (ii), ∠BCA is a right angle. According to the angle sum property of a triangle which states that the sum of interior angles of a triangle is 180.

=> 90° + 55° + x = 180° => x = 180 − 90 − 55 => x = 35°

55

0

x

C

B

A

P

Q

R

x

120

0

2x

Q

P

R

x

25

0

30

0

o

In image (iii), we need to apply the angle sum property of a triangle, according to which

30° + 25° + x = 180° => x = 180° − 30° − 25° => x = 125°

55

0

x

C

B

A

P

Q

R

x

120

0

2x

Q

P

R

x

25

0

30

0