Question

class: vii
date: 10-09-25
l - 5
harnai, waghodia road & manjalpur english medium year : 2025-26 assignment-4 (semester - i) sub. : math date of submission : 16-09-25
l - 5
✶ fill in the blanks.

1. a line segment has ______ end point.
2. the supplementary angle of 45° is ______.
3. ______ angle is formed when one arm is common and remaining two arms are on either side.
4. if a line is a transversal to three lines then ____ points of intersections will be formed.
5. the complementary angle of 54° is ______.
6. the measure of right angle is ______.

✶ do as directed.

1. name the pair of angles in each figure.

(a)
(b)
(c)
(d)

1. find the angle which is equal to its supplement.

✶ in the adjoining figure, identify the following.

1. the pair of alternate interior angles.
2. the pair of corresponding angles.
3. the vertically opposite angles.

✶ find the value of x in the following figure if l || m.
1)
2)
3)
4)
✶ an angle is greater than 90°. is its supplementary angle greater than 90° or equal to 90° or less than 90°? justify.

Explanation:

Fill - in - the - blanks

1)

A line - segment has two end - points.

2)

The sum of supplementary angles is 180°. Let the angle be \(x = 45^{\circ}\), then its supplementary angle \(y=180 - 45=135^{\circ}\).

3)

Adjacent angles are formed when one arm is common and the remaining two arms are on either side.

4)

If a line is a transversal to three lines, then 3 points of intersections will be formed.

5)

The sum of complementary angles is 90°. Let the angle be \(x = 54^{\circ}\), then its complementary angle \(y = 90-54 = 36^{\circ}\).

6)

The measure of a right - angle is \(90^{\circ}\).

Do as directed

1)

(a)

\(\angle1\) and \(\angle2\) are corresponding angles.

(b)

\(\angle3\) and \(\angle4\) are alternate interior angles.

(c)

\(\angle5\) and \(\angle6\) are alternate exterior angles.

(d)

\(\angle7\) and \(\angle8\) are vertically opposite angles.

2)

Let the angle be \(x\). Its supplement is \(180 - x\). If the angle is equal to its supplement, then \(x=180 - x\).

Step1: Add \(x\) to both sides

\(x+x=180 - x+x\), \(2x = 180\).

Step2: Solve for \(x\)

\(x=\frac{180}{2}=90^{\circ}\).

In the adjoining figure

1)

The pair of alternate interior angles are \(\angle3\) and \(\angle5\), \(\angle4\) and \(\angle6\).

2)

The pair of corresponding angles are \(\angle1\) and \(\angle5\), \(\angle2\) and \(\angle6\), \(\angle3\) and \(\angle7\), \(\angle4\) and \(\angle8\).

3)

The vertically opposite angles are \(\angle1\) and \(\angle3\), \(\angle2\) and \(\angle4\), \(\angle5\) and \(\angle7\), \(\angle6\) and \(\angle8\).

Find the value of \(x\)

1)

Since \(l\parallel m\), \(x = 65^{\circ}\) (corresponding angles).

2)

Since \(l\parallel m\), \(x = 70^{\circ}\) (alternate interior angles).

3)

Since \(l\parallel m\), \(x=130^{\circ}\) (corresponding angles).

4)

Since \(l\parallel m\), \(x = 70^{\circ}\) (corresponding angles).

An angle is greater than \(90^{\circ}\)

Let the angle be \(x>90^{\circ}\). Its supplement is \(y=180 - x\).
Since \(x>90^{\circ}\), then \(180 - x<90^{\circ}\) (subtracting \(x\) from 180, when \(x>90\), the result is less than 90).

Answer:

Fill - in - the - blanks

1. two
2. \(135^{\circ}\)
3. Adjacent
4. 3
5. \(36^{\circ}\)
6. \(90^{\circ}\)

Do as directed

1)
(a) Corresponding angles
(b) Alternate interior angles
(c) Alternate exterior angles
(d) Vertically opposite angles

1. \(90^{\circ}\)

In the adjoining figure

1. \(\angle3\) and \(\angle5\), \(\angle4\) and \(\angle6\)
2. \(\angle1\) and \(\angle5\), \(\angle2\) and \(\angle6\), \(\angle3\) and \(\angle7\), \(\angle4\) and \(\angle8\)
3. \(\angle1\) and \(\angle3\), \(\angle2\) and \(\angle4\), \(\angle5\) and \(\angle7\), \(\angle6\) and \(\angle8\)

Find the value of \(x\)

1. \(65^{\circ}\)
2. \(70^{\circ}\)
3. \(130^{\circ}\)
4. \(70^{\circ}\)

An angle is greater than \(90^{\circ}\)

Less than \(90^{\circ}\) because if \(x>90^{\circ}\), then its supplement \(180 - x<90^{\circ}\)