Question

In the given figure, ∠1 = ∠2 then find the measurements of ∠3 and ∠4.

Answer 1

Answer:

angle 1+angle 2+58=180°

angle 1+angle 1=122.......... ∠1 = ∠2

2*angle1=122

angle1=61°

angle 3=180-61

angle 3=119°

angle 4=119°

Answer 2

Given,

Refer figure, one internal angle of the triangle is 58°.

∠1 = ∠2

To find,

∠3 and ∠4

Solution,

The solution to this problem can be simply found using the process given below.

As we know that the sum of all internal angles of a triangle is equal to 180°.

For the given triangle,

∠1 + ∠2 + 58 = 180.

Simplifying,

∠1 + ∠2 = 180 - 58

∠1 + ∠2 = 122

It is given in the question that ∠1 = ∠2. So twice of any of the two angles should equal 122°. Thus,

2*∠1 = 122

⇒ ∠1 = 61°.

As the two angles, ∠1 and ∠2 are equal, so,

∠2 = 61°.

Now, as we can see from figure,  ∠1, ∠3; and ∠2, ∠4 are pairs of linear angles. It means the sum of each pair of these angles will be equal to 180°. So,

∠1 + ∠3 = 180°, and

∠2 + ∠4 = 180°

Substituting the values of ∠1 and ∠2 in the above equations respectively, we get,

∠3 = 180 - ∠1 = 180 - 61 = 119°, and

∠4 = 180 - ∠2 = 180 - 61 = 119°.

Therefore, the values of ∠3 and ∠4 will be 119° for both angles.