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Lines and Angles

    Exercise 5.2

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7th class > Lines and Angles > Exercise 5.2

Exercise 5.2

1. State the property that is used in each of the following statements?

Instruction

If a || b, then ∠1 = ∠5
If ∠4 = ∠6, then a || b
If ∠4 + ∠5 = 180°, then a || b
If pairs of alternate interior angles are equal, the lines are parallel.
If pairs of interior angles on the same side of the transversal are supplementary, the lines are parallel.
Each pair of corresponding angles are equal in measure.

2. In the adjoining figure, identify:

Figure

(i)

(i) the pairs of corresponding angles.

Solution:

From the given figure, the pairs of corresponding angles are: (i) ∠1 and ∠

(ii) ∠ and ∠6

(iii) ∠4 and ∠

(iv) ∠3 and ∠

(ii)

(ii) the pairs of alternate interior angles.

Solution:

From the given figure, the pairs of alternate interior angles are:

(i) ∠3 and ∠

(ii) ∠ and ∠8

(iii)

(iii) The pairs of interior angles on the same side of the transversal.

Solution:

From the given figure, the interior angles on the same side of the transversal are:

(i) ∠3 and ∠

(ii) ∠2 and ∠

(iv)

(iv) the vertically opposite angles.

Solution:

From the given figure, the vertically opposite angles are:

(i) ∠1 and ∠

(ii) ∠ and ∠4

(iii) ∠6 and ∠

(iv) ∠5 and ∠

3. In the adjoining figure, p || q. Find the unknown angles.

Find the values of the unknown angles

Instruction

4. Find the value of x in each of the following figures if l || m

Figure

Solution:

Instruction

We use the geometry concepts like parallel lines, alternate interior angles, supplementary angles, vertically opposite angles and adjacent angles to solve the problem.
(i) Given l || m and t is transversal and ∠y = 110°
∠x + ∠y = ° (Linear pair)
∠x = ° − ° which gives us ∠x = °
(ii) Let’s visually model this problem. There is one operation that can be done. Find the corresponding angle to x. According to this model, the resultant value of the corresponding angle will be equal to x. Now, it’s a matter of finding the measure of x.
Given l || m and a || b,
∠x = ° (corresponding angle)

(i)

5. In the given figure, the arms of two angles are parallel.If ∠ABC = 70º, then find (i) ∠DGC (ii) ∠DEF

Solution:

We use the concepts of parallel lines, supplementary angles, vertically opposite angles and adjacent angles to solve the problem.

(i) ∠DGC

Solve for ∠DGC

Given AB || DG and BC is a transversal.

Also, ∠ABC = ° (Given)

Since, ∠ABC = ∠ (Corresponding angles)

Therefore, ∠DGC = 70° → (1)

(ii)

(ii) ∠DEF

Solution:

Solve for ∠DEF

Given BC || EF and DE is the transversal.

Also, ∠DGC = ° [from (1)]

Since, ∠DGC = ∠ (Corresponding angles)

Therefore, ∠DEF = 70°

6. In the given figures below, decide whether l is parallel to m.

Instruction