Question

5. A transversal intersects two parallel lines. Ratio of interior angles formed
on same side of transversal is 2:7. Find measures of the greater angle.​

Answer 1

Answer:

140°

Step-by-step explanation:

Let the angle formed be x

According to the theorem of parellel in and transversal

the interior angles are supplementary

2x + 7x = 180°

9x = 180°

x = 180/9

x = 20° –––––1

According to equation 1 ;

7x = 7 × 20

= 140°

the greater interior angle is 140°

Answer 2

Answer:

The answer will be 140° as the measure of the greater angle.

Step-by-step explanation:

We've given;

                  Transversal intersecting two parallel lines.

                   Ratio of interior angles(on the same side) = 2:7;

We know that when a transversal passes through two parallel lines there's form two alternate interior angles where each of them forms complimentary to another.

Lets, consider the angle in linear pair formed on one of parallel line be ∠A and ∠B. Now, consider the angle in linear pair on the another parallel line be ∠C and ∠D.

Hence, ∠A + ∠B = 180;                                (i)

            ∠C + ∠D= 180;                               (ii)

Now, ∠A = ∠D (Because they are alt. int. ∠s)                               (iii)

Similarly, ∠B = ∠C (Because they are alt. int. ∠s)                             (iv)

According to given ratio, let ∠B and ∠D be 2x and 7x because this is what the question is saying (angles on one side. It could either be ∠A and ∠C).

Using equation (i) and (iii), it can be deduced that;

                   = ∠D + ∠B = 180;

                   = 7x + 2x = 180;

                   = 9x = 180;

                   = x = 180/9;

                   = x = 20;

Hence, ∠B = 2x = 2(20) = 40;

             ∠C = ∠B = 40;

             ∠D = 7x = 7(20) = 140;

             ∠A = ∠D = 140;

Hence, the measure of greater angle will be 140.

That's all.