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1.

The following figures GUNS and RUNS are parallelograms.Find x and y. (Lengths are in cm)

Answer» We know opposite sides of parallelogram are same.
1)3x=18
x=6.
3y-1=26
3y=27
y=27
diagonals of a parallelogram intersect each other from mid point
2)y+7=20
y=13
x+y=16
x=3.
Discussion
2.

Find the measure of each exterior angle of a regular polygon of(i) 9 sides (ii) 15 sides

Answer» Sum of all exterior angles of a regular polyfon is `360^@`.
If `n` is number of sides and `x` is its exterior angle. Then,
`nx = 360^@`
(i) Here, `n = 9`
So, Exterior angle, `x = 360/9 = 40^@`

(ii) Here, `n = 15`
So, Exterior angle, `x = 360/15 = 24^@`
Discussion
3.

Find the perimeter of the parallelogram PQRS (Fig 3.22).

Answer» Perimeter of a parallelogram = 2*Sum of unequal sides
So, Perimeter of given parallelogram `PQRS`, `P_r= 2**(PQ+QR)`
`P_r = 2**(12+7) = 2**19 = 38cm`
Discussion
4.

Explain how this figure is a trapezium. Which of its two sides are parallel? (Fig 3.32)

Answer» sides whose sum of angles are `180^0` are parallel.
Discussion
5.

Find the number of sides of a regular polygon whose each exterior angle has a measure of `45^@`.

Answer» Number of sides of a regular polygon = 360/Exterior angle
Here, Exterior angle = `45^@`
So, Number of sides of a regular polygon, `s = 360/45 = 8`
Discussion
6.

Find `m angleC` in fig 3.33 if `AB||DC`

Answer» We know,
`angleABC+angleBCD=180^0`
`angleBCD=180-120`
`angleBCD=60^0`.
Discussion
7.

In Fig 3.26, BEST is a parallelogram. Find the values x, y and z.

Answer» As, opposite angles of a parallelogram are always equal. So,
`/_S = /_B => x = 100^@`
Also, sum of interior angles of a parallelogram is `180^@`.
So, `x+z = 180^@=> 100^@+z = 180^@=> z = 80^@`
Now, `y` and `z` are supplementary angles as they are on a straight line.
So, `y+z = 180^@=> y+80^@ = 180^@=> y = 100^@`
Discussion
8.

Given a parallelogram `ABCD.` Complete each statement along with the definition or property used. (i) `AD=` (ii) `< DCB=` (iii) `OC=` (iv) `m < DAB+m < CDA`

Answer» In a parallelogram opposite sides and angles are equal.
So,
(i) `AD = BC`
(ii)`/_DCB = /_BAD`
(iii)`OC = OA` (As diagonals of a parallelogram bisects each other)
(iv)`/_DAB+/_CDA = /_DCB+/_ABC = 180^@`
Discussion
9.

How many sides does a regular polygon have if each of its interior angles is `165^@` ?

Answer» Let number of sides of given regular polygon is `n`.
Then, sum of all of the angles can be given as,
`S = (n-2)**180^@->(1)`
Also, as we are given each interior angle is `165^@`,
So, Sum of all the angles will also be,
`S = 165n->(2)`
From (1) and (2),
`(n-2)**180 = 165n`
`180n - 360 = 165n => 15n = 360 => n = 360/15 = 24`
So, number of sides in the given polygon is `24`.
Discussion