The angles of a quadrilateral are 4x, 7x, 15x and 10x. Find the smallest and the largest angles of the quadrilateral
Question
The angles of a quadrilateral are 4x, 7x, 15x and 10x. Find the smallest and the largest angles of the quadrilateral
Solution
Sure, let's solve this step by step:
Step 1: We know that the sum of the angles in a quadrilateral is 360 degrees.
Step 2: So, we can set up the equation 4x + 7x + 15x + 10x = 360.
Step 3: Simplify the left side of the equation to get 36x = 360.
Step 4: Solve for x by dividing both sides of the equation by 36 to get x = 10.
Step 5: Substitute x = 10 back into the expressions for the angles to get the actual degree measures:
- The smallest angle is 4x = 4*10 = 40 degrees.
- The largest angle is 15x = 15*10 = 150 degrees.
So, the smallest angle of the quadrilateral is 40 degrees and the largest angle is 150 degrees.
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