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.
Question
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.
Solution
Sure, let's solve this step by step.
Step 1: We know that the sum of all angles in a quadrilateral is 360 degrees.
Step 2: Given that the sum of the largest and smallest angle is 200 degrees, the sum of the other two angles is 360 - 200 = 160 degrees.
Step 3: The ratio of the other two angles is given as 3:7. This means the two angles can be represented as 3x and 7x.
Step 4: Since the sum of these two angles is 160 degrees, we can write the equation 3x + 7x = 160.
Step 5: Solving this equation gives x = 160 / 10 = 16.
Step 6: Therefore, the two angles are 316 = 48 degrees and 716 = 112 degrees.
Step 7: The difference between these two angles is 112 - 48 = 64 degrees.
So, the difference between the other two angles is 64 degrees.
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