Question

1. In the given figure, the value of x is
(1) 35°
(2) 45°
(3) 50°
(4) 60°​

Answer 1

Answer:

Step-by-step explanation:

7y+5y=180 (linear pair )

12y=180

y=15

so angle cba= 15(5)= 75

and angle bca= 3(15)=45

also 45+75+x=180

x=180-120

x=60

Answer 2

Answer:

(4) 60°

Step-by-step explanation:

Taking ∠DBC and ∠CBA,

∠DBC + ∠CBA = 180° [Adjacent Angles]

7y + 5y = 180°

12y = 180°

y = $\frac{180}{12}$

y = 15

∴ ∠CBA = 5y

             = 5 * 15

    ∠CBA = 75°

∴ ∠ACB = 3y

             = 3 * 15

    ∠ACB = 45°

In ΔABC,

∠CBA + ∠ACB + ∠BAC = 180° [Sum of vertex angles in a triangle is always 180°]

75° + 45° + ∠x = 180°

120° + ∠x = 180°

∠x = 180° - 120°

∠x = 60°