please give answer of these questions with explanation
Answers
Answer:
3) x = 25 degree
y = 115 degree
z = 115 degree
4) p = 145 degree
x =35 degree
y = 75 degree
z = 70 degree
Step-by-step explanation:
Answer:-
1)
- ∠x = 25°
- ∠y = 115°
- ∠z = 115°
2)
- ∠p = 145°
- ∠y = 75°
- ∠z = 70 degree
Explanation:-
Q-1
Given :
- ∠a = 3x - 10°
- ∠b = 2x + 15
To Find :
- ∠y
- ∠x
- ∠z
Solution :
3x - 10° = 2x + 15° [vertically opposite angles are equal]
⇒ 3x - 2x = 15° + 10°
∴ x = 25
3x - 10 + y = 180 [linear pair]
⇒ 3(25) - 10 + y = 180
⇒ 75 - 10 + y = 180
⇒ 65 + y = 180
⇒ y = 180 - 65
∴ ∠y = 115°
z + 2x + 15 = 180
⇒ z + 2(25) + 15 = 180
⇒ z + 50 + 15 = 180
⇒ z + 65 = 180
⇒ z = 180 - 65
∴ ∠z = 155°
Q-2
Given :
- ∠a = 70°
- ∠b = 35°
To Find :
- ∠x
- ∠y
- ∠p
Solution :
∠a = 70°
Therefore ∠c = 70° [vertically opposite angles are equal]
∠c + ∠b + ∠y = 180° [Angle sum property]
⇒ 70° + 35° + ∠y = 180°
⇒ 105° + ∠y = 180°
⇒ ∠y = 180° - 105°
∴ ∠y = 75°
∠a = 70°
∴ ∠z = 70° [corresponding angles are equal]
∠z + ∠y + ∠x = 180° [Angle sum property]
⇒ 70° + 75 + ∠x = 180°
⇒ 145° + ∠x =180°
⇒ ∠x =180° - 145°
∴ ∠x = 35°
