Question

∠PBC = 70°, ∠CND = 36° and PQ || RS. Find the value of x.

Answer 1

Given:

∠PBC = 70°

∠CND = 36°

PQ || RS Lines are parallel

We are asked to find x likely an angle formed by transversals intersecting the parallel lines

Step 1: Use the property of parallel lines

When two lines are parallel, the angles formed by a transversal satisfy these properties:

1. Corresponding angles are equal
2. Alternate interior angles are equal
3. Co-interior same-side interior angles add up to 180°

Step 2: Identify the angles

Suppose x = ∠BCR, formed at the intersection of transversals with PQ || RS

Then ∠PBC = 70° is one angle at the top of the transversal

∠CND = 36° is the other angle

We need to find the angle on the same side of a straight line:

x + ∠PBC + ∠CND = 180°

Step 3: Substitute the given values

x + 70 + 36 = 180

x + 106 = 180

x = 74°

Step 4: Correct reasoning

The total angle on a straight line is 180°

If x is the exterior angle corresponding to ∠PBC and ∠CND, then:

x = 180 – (∠PBC + ∠CND)

x = 180 – (70 + 36)

x = 180 – 106

x = 74°

So maybe x is supplementary to the sum of the two angles, meaning:

x = ∠PBC + ∠CND

= 70 + 36

= 106°