Question

Find the unknown angles​

Answer 1

a)

Let's take

• 45° = A

• 70° = B

• 30° = C

We know that,

• Sum of all interior angles of a triangle is 180°

• A + Y + B = 180°

• 45° + Y + 70° = 180°

• 115° + Y = 180°

• Y = 180° - 115°

• Y = 65°

Y = 65°

We know that,

• Sum of linear pair is 180°

• Y + Z = 180°

• 65° + Z = 180°

• Z = 180° - 65°

• Z = 115°

Z = 115°

We know that,

• Sum of all interior angles of a triangle is 180°

• X + C + Z = 180°

• X + 30° + 115° = 180°

• X + 145° = 180°

• X = 180° - 145°

• X = 35°

X = 35°

___________________________

b)

Let's take

• 60° = A

• Right angle = B

• Right angle = C

• Y = Z

We know that,

• Sum of all interior angles of a triangle is 180°

• X + A + C = 180°

• X + 60° + 90° = 180°

• X + 150° = 180°

• X = 180° - 150°

• X = 30°

X = 30°

We know that,

• Sum of all interior angles of a triangle is 180°

• B + Y + Z = 180°

• 90° + Y + Z = 180°

• Y + Z = 180° - 90°

• Y + Z = 90°

• Y = 90° / 2

• Y= 45°

• Z = 45°

Y= 45°

Z = 45°

___________________________

c)

Let's take

• 60° = B

• 70° = C

• 120° = D

We know that,

• Sum of linear pair is 180°

• B + C + Z = 180°

• 60° + 70° + Z = 180°

• Z = 180° - 130°

• Z = 50°

Z = 50°

We know that,

• Sum of linear pair is 180°

• X + D = 180°

• X + 12O° = 180°

1. X = 180° - 120°

• X = 60°

X = 60°

We know that,

• Sum of all interior angles of a triangle is 180°

X + Y + B = 180°

60° + Y + 60° = 180°

120° + Y = 180°

Y = 180° - 120°

Y = 60°

Y = 60°

We know that,

• Sum of all interior angles of a triangle is 180°

• Z + D + A = 180°

• 50° + 120° + A = 180°

• 170° + A = 180°

• A = 180° - 170°

• A = 10°

A = 10°

___________________________

d)

Let's take

3x + 1 = A

2x = B

2x + 4 = C

We know that,

• Sum of all interior angles of a triangle is 180°

• A + B + C = 180°

• ( 3x + 1 ) + ( 2x ) + ( 2x + 4 ) = 180°

• 7x + 5° = 180°

• 7x = 180° - 5°

• 7x = 175°

• x = 175 / 7

• x = 25

x = 25°

We know that,

• 3x + 1 = A

• A = 3 × 25 + 1

• A = 75° + 1°

• A = 76°

A = 76°

We know that,

• 2x = B

• B = 2 × 25°

• B = 50°

B = 50°

We know that,

• 2x + 4 = C

• C = 2 × 25 + 4

• C = 50° + 4°

• C = 54°

C = 54°