Question

5. An exterior angle of a parallelogram is 110°. Find the angles of the parallelogram.
6. Two adjacent sides of a parallelogram are in the ratio 3:8 and its perimeter is 110 cm. Find
the sides of the parallelogram.​

Answer 1

Question:

• 5. An exterior angle of a parallelogram is 110°. Find the angles of the parallelogram.
• 6. Two adjacent sides of a parallelogram are in the ratio 3:8 and its perimeter is 110 cm. Find the sides of the parallelogram.​

Answer:

• 70°, 70°, 110°, 110°

• 15cm, 40cm , 15cm , 40cm

Step-by-step explanation:

• Let ABCD is a parallelogram,

Such that,

After expanding the side DC through C to O,

⇒ m∠BCO = 110°,

∵ m∠BCD + m∠BCO = 180°

⇒ m∠BCD + 110° = 180°

⇒ m∠BCD = 70°

Since,

in a parallelogram the opposite interior angles are equal,

That is,

m∠BCD = m∠BAD

and m∠ADC = m∠ABC,

Also, sum of all interior angles of a quadrilateral is 360°,

⇒ m∠BCD + m∠BAD + m∠ADC + m∠ABC = 360°

70° + 70° + m∠ADC + m∠ADC  = 360°

140° + 2m∠ADC  = 360°

2m∠ADC = 220°

m∠ADC = 110°

⇒ m∠ABC= 110°

• ratio of two adjacent sides = 3 : 8

let the constant ratio be 'x'

let the adjacent sides are 3x. , 8x

perimeter = 110cm

2( sum of adjacent sides) = 110cm

2( 3x + 8x) = 110

22x = 110 => x = 5

thus ,

adjacent sides are 3x = 3× 5 = 15cm

and 8x = 8 × 5 = 40cm

since we know opposite sides of parallelogram are equal.

so then , other two sides of parallelogram are

15cm, 40cm

All the sides of parallelogram are

15cm, 40cm , 15cm , 40cm