Question 1:

A triangle ABC has ∠ABC = 13° and ∠BCA = 36°. Calculate ∠CAB

Solution:

According to the Triangle Sum Theorem, the interior angles of a triangle add up to 180°

Therefore, ∠ABC + ∠BCA + ∠CAB = 180°

=> 13° + 36° + ∠CAB = 180°

=> 49° + ∠CAB = 180°

=> ∠CAB = 180° - 49°

=> ∠CAB = 131° (Ans)

Question 2:

An isosceles triangle has one triangle = 56°. What are the remaining angles if they are equal angles?

Solution:

According to the Triangle Sum Theorem, the interior angles of a triangle add up to 180°

Let us assume that the triangle is ABC,

where ∠ABC = 56° and ∠BCA = ∠CAB = x°

Therefore, ∠ABC + ∠BCA + ∠CAB = 180°

=> 56° + x + x = 180°

=> 56° + 2x = 180°

=> 2x = 180° - 56°

=> 2x = 124°

=> ∠BCA = ∠CAB = 62° (Ans)

Question 3:

A right-angled triangle has one angle equal to 43°. What is the value of the other angles?

Solution:

According to the Triangle Sum Theorem, the interior angles of a triangle add up to 180°

Let us assume that the triangle is ABC,

where ∠ABC = 90° (as the triangle is right angled) and ∠BCA = 43°

Therefore, ∠ABC + ∠BCA + ∠CAB = 180°

=> 90° + 43° + ∠CAB = 180°

=> 133° + ∠CAB = 180°

=> ∠CAB = 180° - 133°

=> ∠CAB = 47° (Ans)

Question 4:

Find the angles of a triangle where the second angle is twice the first angle and the third angle is one-third the first angle.

Solution:

Let us consider the first angle as x. Then the 2nd angle is 2x and the third is (1/3)x

According to the Triangle Sum Theorem, the interior angles of a triangle add up to 180°

Therefore, x + 2x+ (1/3)x = 180°

=> 3x + (1/3)x = 180°

=> (10/3)x = 180°

=> x = 180° X 3/10 = 18 X 3 = 54°

Thus 1st angle is 54°; 2nd angle is 108° and 3rd angle is 18° (Ans)