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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° – x
∴  x + 14° = 90° – x
x + x = 90° – 14° ⇒  2x = 76°
⇒ x = = 38°
∴  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
∴  Its supplementary angle = 180° – x
∴  x = 2(180°-x) = 360°-2x
⇒  x + 2x = 360°
⇒ 3x = 360°
⇒  x == 120°
∴  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° – x
and supplement angle = 180° – x
∴  3(90° – x) = 180° – x
⇒ 270° – 3x = 180° – x
⇒270° – 180° = -x + 3x => 2x = 90°
⇒ x = 45°
∴  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°-  x
and supplement = 180° – x
∴  180°-x = 3(90°-x)
⇒  180° – x = 270° – 3x
⇒  -x + 3x = 270° – 180°
⇒ 2x = 90° ⇒ x ==45°
∴ Required angle = 45°

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