Question

ambe group of schools, vadodara
harni, waghodia road & manjalpur
english medium year : 2025 - 26
assignment - 4 (semester - i)
sub. : math
class: vii
date : 10 - 09 - 25
date of submission : 16 - 09 - 25
l - 5
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 endpoints. This is a basic definition in geometry.

2.

The supplementary angle of an angle $\theta$ is $180^{\circ}-\theta$. For $\theta = 45^{\circ}$, the supplementary angle is $180 - 45=135^{\circ}$.

3.

A linear - pair angle is 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 three points of intersections will be formed.

5.

The complementary angle of an angle $\alpha$ is $90^{\circ}-\alpha$. For $\alpha = 54^{\circ}$, the complementary angle is $90 - 54 = 36^{\circ}$.

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 vertically opposite angles.

(c)

$\angle5$ and $\angle6$ are alternate interior angles.

(d)

$\angle7$ and $\angle8$ are adjacent 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: Divide both sides by 2

$x=\frac{180}{2}=90^{\circ}$

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.

The angle adjacent to $130^{\circ}$ on line $l$ is $180 - 130=50^{\circ}$. Since $l\parallel m$, $x = 50^{\circ}$ (corresponding angles).

4.

The angle adjacent to $110^{\circ}$ on line $m$ is $180 - 110 = 70^{\circ}$. Since $l\parallel m$, $x=70^{\circ}$ (corresponding angles).

Justify:

Let the angle $\theta>90^{\circ}$. Its supplementary angle $\beta=180-\theta$.
Since $\theta>90^{\circ}$, then $180-\theta<90^{\circ}$. So the supplementary angle of an angle greater than $90^{\circ}$ is less than $90^{\circ}$.

Answer:

Fill - in - the - blanks:

1. two
2. $135^{\circ}$
3. linear - pair
4. three
5. $36^{\circ}$
6. $90^{\circ}$

Do as directed:

1. (a) corresponding angles; (b) vertically opposite angles; (c) alternate interior angles; (d) adjacent angles
2. $90^{\circ}$

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. $50^{\circ}$
4. $70^{\circ}$

Justify:

The supplementary angle is less than $90^{\circ}$ because if $\theta>90^{\circ}$, then $180 - \theta<90^{\circ}$.