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RD Chapter 10 Congruent Triangles Ex 10.1 Solutions

Question - 1 : -
Write the complement of each of the following angles:
(i) 20┬░
(ii) 35┬░
(iii) 90┬░
(iv) 77┬░
(v) 30┬░

Answer - 1 : -

We know that two angles are complement to each other if their sum is 90┬░. Therefore,
(i) Complement of 20┬░ is (90┬░ тАУ 20┬░) = 70┬░
(ii) Complement of 35┬░ is (90┬░ тАУ 35┬░) = 55┬░
(iii) Complement of 90┬░ is (90┬░ тАУ 90┬░) = 0┬░
(iv) Complement of 77┬░ is (90┬░ тАУ 77┬░) = 13┬░
(v) Complement of 30┬░ is (90┬░ тАУ 30┬░) = 60┬░

Question - 2 : -
Write the supplement of each of the following angles:
(i) 54┬░
(ii) 132┬░
(iii) 138┬░

Answer - 2 : -

We know that two angles are supplement to each other if their sum if 180┬░. Therefore,
(i) Supplement of 54┬░ is (180┬░ тАУ 54┬░) = 126┬░
(ii) Supplement of 132┬░ is (180┬░ тАУ 132┬░) = 48┬░
(iii) Supplement of 138┬░ is (180┬░ тАУ 138┬░) = 42┬░

Question - 3 : - If an angle is 28┬░ less than its complement, find its measure.

Answer - 3 : -

Let required angle = x, then
Its complement = x + 28┬░
тИ┤┬а x + x + 28┬░ = 90┬░ тЗТ┬а 2x = 90┬░ тАУ 28┬░ = 62┬░
тИ┤ x =┬а┬а= 31┬░
тИ┤ Required angle = 31┬░

Question - 4 : - If an angle is 30┬░ more than one half of its complement, find the measure of the angle.

Answer - 4 : -

Let the measure of the required angle = x
тИ┤┬а Its complement =┬а 90┬░ тАУ x
тИ┤┬а x =┬а(90┬░ тАУ x) + 30┬░
2x = 90┬░ тАУ x + 60┬░
тЗТ 2x + x = 90┬░ + 60┬░
тЗТ┬а 3x = 150┬░
тЗТ x =┬а= 50┬░
тИ┤ Required angle = 50┬░

Question - 5 : - Two supplementary angles are in the ratio 4 : 5. Find the angles.

Answer - 5 : -

Ratio in two supplementary angles = 4 : 5
Let first angle = 4x
Then second angle = 5x
тИ┤┬а 4x + 5x = 180
тЗТ┬а 9x = 180┬░
тИ┤ x┬а == 20┬░
тИ┤┬а First angle = 4x = 4 x 20┬░ = 80┬░
and second angle = 5x
= 5 x 20┬░ = 100┬░

Question - 6 : - Two supplementary angles differ by 48┬░. Find the angles.

Answer - 6 : -

Let first angle = x┬а ┬а ┬а ┬а ┬а ┬а ┬а ┬а ┬а ┬а ┬а ┬а тАЭ
Then second angle = x + 48┬░
тИ┤┬а x + x + 48┬░ = 180┬░тЗТ┬а 2x + 48┬░ = 180┬░
тЗТ┬а 2x = 180┬░ тАУ 48┬░ = 132┬░
x=┬а┬а=66┬░
тИ┤┬а First angle = 66┬░
and second angle = x + 48┬░ = 66┬░ + 48┬░ = 114┬░
тИ┤ Angles are 66┬░, 114┬░

Question - 7 : - An angle is equal to 8 times its complement. Determine its measure.

Answer - 7 : -

Let the required angle = x
Then its complement angle = 90┬░ тАУ x
тИ┤ x = 8(90┬░ тАУ x)
тЗТ x = 720┬░ тАУ 8x тЗТ┬а x + 8x = 720┬░
тЗТ 9x = 720┬░ тЗТ x == 80┬░
тИ┤┬а Required angle = 80┬░

Question - 8 : - If the angles (2x тАУ 10)┬░ and (x тАУ 5)┬░ are complementary angles, find x.

Answer - 8 : -

First complementary angle = (2x тАУ 10┬░) and second = (x тАУ 5)┬░
тИ┤ 2x тАУ 10┬░ + x тАУ 5┬░ = 90┬░
тЗТ 3x тАУ 15┬░ = 90┬░ тЗТ┬а 3x = 90┬░ + 15┬░ = 105┬░
тИ┤ x == 35┬░
тИ┤┬а First angle = 2x тАУ 10┬░ = 2 x 35┬░ тАУ 10┬░
= 70┬░ тАУ 10┬░ = 60┬░
and second angle = x тАУ 5 = 35┬░ тАУ 5 = 30┬░

Question - 9 : - If an angle differ from its complement by 10┬░, find the angle.

Answer - 9 : -

Let required angle = x┬░
Then its complement angle = 90┬░ тАУ x┬░
тИ┤ x тАУ (90┬░ тАУ x) = 10
тЗТ┬а x тАУ 90┬░ + x = 10┬░тЗТ┬а 2x = 10┬░ + 90┬░ = 100┬░ 100┬░
тЗТ x == 50┬░
тИ┤ Required angle = 50┬░

Question - 10 : - If the supplement of an angle is two-third of itself Determine the angle and its supplement.

Answer - 10 : -

Let required angle = x
Then its supplement angle = 180┬░ тАУ x
тИ┤┬а (180┬░-x)=┬а┬аx
540┬░ тАУ 3x = 2x тЗТ 2x + 3x = 540┬░
тЗТ 5x = 540┬░тЗТ┬а x == 108┬░
-. Supplement angle = 180┬░ тАУ 108┬░ = 72┬░

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