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RD Chapter 10 Congruent Triangles Ex 10.1 Solutions

Question - 11 : - An angle is 14┬░ more than its complementary angle. What is its measure?

Answer - 11 : -

Let required angle = x
Then its complementary angle = 90┬░ тАУ x
тИ┤┬а x + 14┬░ = 90┬░ тАУ x
x + x = 90┬░ тАУ 14┬░ тЗТ┬а 2x = 76┬░
тЗТ x =┬а= 38┬░
тИ┤┬а Required angle = 38┬░

Question - 12 : - The measure of an angle is twice the measure of its supplementary angle. Find its measure.

Answer - 12 : -

Let the required angle = x
тИ┤┬а Its supplementary angle = 180┬░ тАУ x
тИ┤┬а x = 2(180┬░-x) = 360┬░-2x
тЗТ┬а x + 2x = 360┬░
тЗТ 3x = 360┬░
тЗТ┬а x == 120┬░
тИ┤┬а Required angle = 120┬░

Question - 13 : - If the complement of an angle is equal to the supplement of the thrice of it. Find the measure of the angle.

Answer - 13 : -

Let required angle = x
Then its complement angle = 90┬░ тАУ x
and supplement angle = 180┬░ тАУ x
тИ┤┬а 3(90┬░ тАУ x) = 180┬░ тАУ x
тЗТ 270┬░ тАУ 3x = 180┬░ тАУ x
тЗТ270┬░ тАУ 180┬░ = -x + 3x => 2x = 90┬░
тЗТ x = 45┬░
тИ┤┬а Required angle = 45┬░

Question - 14 : - If the supplement of an angle is three times its complement, find the angle.

Answer - 14 : -

Let required angle = x
Then its complement = 90┬░-┬а x
and supplement = 180┬░ тАУ x
тИ┤┬а 180┬░-x = 3(90┬░-x)
тЗТ┬а 180┬░ тАУ x = 270┬░ тАУ 3x
тЗТ┬а -x + 3x = 270┬░ тАУ 180┬░
тЗТ 2x = 90┬░ тЗТ x ==45┬░
тИ┤ Required angle = 45┬░

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