he largest and the second largest angles of a triangle are in the ratio of 3 : 2 respectively. The smallest angle is 20% of the sum of the rest two angles. What is the sum of the smallest and the second largest angles?Choices:- 80° 60° 100° 90°
Question
he largest and the second largest angles of a triangle are in the ratio of 3 : 2 respectively. The smallest angle is 20% of the sum of the rest two angles. What is the sum of the smallest and the second largest angles?Choices:- 80° 60° 100° 90°
Solution
Let's solve this step by step:
Step 1: Let's assume the largest angle is 3x and the second largest angle is 2x.
Step 2: According to the problem, the smallest angle is 20% of the sum of the largest and second largest angles. So, the smallest angle = 20/100 * (3x + 2x) = x.
Step 3: We know that the sum of angles in a triangle is 180°. So, 3x + 2x + x = 180°. Solving this we get x = 30°.
Step 4: Now, the smallest angle is x = 30° and the second largest angle is 2x = 60°.
Step 5: The sum of the smallest and the second largest angles is 30° + 60° = 90°.
So, the answer is 90°.
Similar Questions
The sum of the largest and the smallest angle of a quadrilateral is 200∘200 ∘ . The ratio of the other two angles is 3:73:7. Find the corresponding difference of the other two angles.
he largest angle of a triangle is opposite the side, and the smallest angle is opposite the side.
The ratio between the three angles of a quadrilateral is 12 : 9 : 6 respectively. The value of the fourth angle of the quadrilateral is 36°. What is the difference between the largest and the second smallest angles of the quadrilateral?
A triangle has sides of length 10 cm, 8 cm and 9 cm.(a) Calculate, in degrees to the nearest 0.1∘ , the size of the largest angle of this triangle.(b) Find, to 3 significant figures, the area of this triangle.
Two angles of a hexagon are 120 oand 100 o . If the remaining four angles are equal, then find its smallest angle.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.