Three interior angles of a convex heptagon measure 125 degrees, and two of the interior angles measure 143 degrees. Which are possible measures for the other two interior angles of the heptagon?
1: 48 and 48 degrees
2: 39 and 100 degrees
3: 100 and 116 degrees
4: 89 and 150 degrees
So which is the answer(1) (2) (3) or (4)
Answer: 89 & 150
Explanation: here what i did, you know that a heptagon has 7 sides it gives you 5 angles out of 7 .
is says 3 sides have 125° (125 *3= 375). then it also says another two angles of the heptagon has 143° same thing as before (143*2=286)
Add the products of the equations giving you the sum of 661. Since 180*5 =900 just add 661 with the answer choices it gives you, to find the one that has 900. Which is number (4) 89 & 150.
Hope this helps im bad at explaining things...
Isn't the sum for the interior angles of a polygon 180(n-2) ?
and a heptagon is n=7, right?
Yes it is
I got it thank you :)
Thanks! This helped a lot.
To determine the possible measures for the other two interior angles of the heptagon, we can start by finding the sum of the angles in the heptagon.
A convex heptagon has seven sides and thus seven interior angles. The sum of the interior angles of any polygon can be found using the formula (n-2) * 180 degrees, where n represents the number of sides. Therefore, the sum of the interior angles of the heptagon is (7-2) * 180 = 5 * 180 = 900 degrees.
We already know that three interior angles measure 125 degrees each, and two interior angles measure 143 degrees each. Therefore, the sum of these five angles is 3 * 125 + 2 * 143 = 375 + 286 = 661 degrees.
To determine the remaining sum of the two unknown angles, we subtract the sum of the five known angles from the sum of all the interior angles of the heptagon: 900 - 661 = 239 degrees.
Now, looking at the answer choices, we can check if any pair of angles adds up to 239 degrees.
1. 48 + 48 = 96 degrees (not equal to 239)
2. 39 + 100 = 139 degrees (not equal to 239)
3. 100 + 116 = 216 degrees (not equal to 239)
4. 89 + 150 = 239 degrees (equal to 239)
Therefore, the possible measures for the other two interior angles of the heptagon are 89 and 150 degrees. Hence, the correct answer is option 4: 89 and 150 degrees.