Lines and Angles Test

Result

Lines and Angles Test - 8

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Question 1
1 / -0

If the angles of an isosceles triangle are in the ratio 1 : 2 : 1, then find the measures of the three angles.

A
30°, 60°, 30°

B
40°, 80°, 40°

C
45°, 90°, 45°

D
35°, 80°, 35°

Solution

Let the angles of the isosceles triangle ABC be ∠A = x, ∠B = 2x and ∠C = x.
Sum of all the angles of a triangle is 180°.
So, in ΔABC, ∠A + ∠B + ∠C = 180°
⇒ x + 2x + x = 180°
⇒ 4x = 180° or x = 45°
Thus, the angles of the triangle are 45°, 90°and 45°.
Question 2
1 / -0

If two angles of a triangle are acute angles, then the third angle will always be _____.

A
an acute angle

B
an obtuse angle

C
a right angle

D
Any of the three

Solution

All angles are measured in degrees.

Case 1: If the sum of two angles is 90°, then the third angle must be 90°. (Right angle)

Example: Two angles are: 30° and 60°.
Then, the third angle must be 90°. (Right angle)

Case 2: If the sum of two angles is less than 90°, then the third angle must be greater than 90°. (Obtuse angle)

Example: Two angles are: 30° and 50°.
Then, the third angle must be 100°. (Obtuse angle)

Case 3: If the sum of two angles is greater than 90°, then the third angle must be less than 90°. (Acute angle)

Example: Two angles are: 30° and 80°.
Then, the third angle must be 70°. (Acute angle)