In a triangle, one angle is 90°. Then
(i) The other two angles are of 45° each
(ii) In remaining two angles, one angle is 90° and other is 45°
(iii) Remaining two angles are complementary. In the given option(s) which is true?
(i) only
(ii) only
(iii) only
(i) and (ii)
Solution:
Given, in a triangle one angle is 90°.
We have to find the other two angles.
(i) considering the other two angles are 45° each
By angle sum property of a triangle,
We know that the sum of all the three interior angles of the triangle is equal to 180 degrees.
Sum of angles = 90° + 45° + 45°
= 90° + 90°
= 180°
(ii) considering one angle is 90° and other is 45°
Sum of angles = 90° + 90° + 45°
= 180° + 45°
= 225° > 180°
Therefore, the other two angles cannot be 90° and 45°
(iii) considering the other two angles are complementary
When the sum of measures of two angles is equal to 90 degrees, then the angles are called complementary angles.
By angle sum property of a triangle,
∠A + ∠B + ∠C = 180°
∠A + 90 + ∠C = 180°
∠A + ∠C = 180° - 90°
∠A + ∠C = 90°
Therefore, the other two angles are complementary.
✦ Try This: In an isosceles triangle, one angle is 100°. The other two angles are
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 6
In a triangle, one angle is 90°. Then (i) The other two angles are of 45° each, (ii) In remaining two angles, one angle is 90° and other is 45°, (iii) Remaining two angles are complementary. In the given option(s) which is true? a. (i) only, b. (ii) only, c. (iii) only, d. (i) and (ii)
Summary:
In a triangle, one angle is 90°. Then the remaining two angles are complementary
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