Question

13. In the given figure, ∠1 = ∠2 then the measurements of ∠3 and ∠4 are:​

Answer 1

Answer:

d) 119, 119

Step-by-step explanation:

Let angle 1 = angle 2 = x

Sum of all angles of a triangle = 180 (Angle sum property)

Therefore,

58 + angle 1 + angle 2 = 180

58 + x + x = 180

58 + 2x = 180

2x = 122

x = 61

Hence,

angle 1 = angle 2 = 61

angle 1 + angle 3 = 180 (Linear Pair)

61 + angle 3 = 180

angle 3 = 119

In the same way, angles 4 and 2 form a linear pair, and since angle 2 = angle 1, angle 4 = angle 3 = 119

Ans: Angles 3 and 4 both are equal to 119.

Hope this helps!

Answer 2

✬ ∠3 = ∠4 = 119° ∠3

Step-by-step explanation:

Given:

• ∠1 = ∠2

To Find:

• Measurements of ∠3 and ∠4 ?

Solution: Let ∠1 = ∠2 = x.

Now, in triangle by angle sum property

★ Sum of all angles of ∆ = 180° ★

$\implies{\rm }$ 58° + x + x = 180°

$\implies{\rm }$ 58° + 2x = 180°

$\implies{\rm }$ 2x = 180° – 58°

$\implies{\rm }$ 2x = 122

$\implies{\rm }$ x = 122/2

$\implies{\rm }$ x = 61°

So measure of

• ∠1 is 61°.
• ∠2 is 61°.

Now ∠1 & ∠3 are liner pair angles.

★ Sum of Linear pair angles = 180° ★

∴ ∠1 + ∠3 = 180°

➮ 61° + ∠3 = 180°

➮ ∠3 = 180° – 61° = 119°

Similarly ∠4 will be also 119°.