To find the value of x in this problem, we can use the property that the exterior angle of a triangle is equal to the sum of its remote interior angles. Here's how we can set up and solve the equation:
1. Given: - Exterior angle = (5x + 9)° - Remote interior angles = 33° and (2x)°
2. According to the property mentioned above, we have: (5x + 9) = 33 + (2x)
3. Now, let's solve for x by isolating it on one side of the equation: 5x + 9 = 33 + 2x 5x - 2x = 33 - 9 3x = 24 x = 24 / 3 x = 8
Therefore, the value of x in this case is 8. This makes the exterior angle equal to (5(8) + 9)° = 49°, and the remote interior angles equal to 33° and (2(8))° = 16°.
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Answer:
To find the value of x in this problem, we can use the fact that the sum of the exterior angle of a triangle is equal to the sum of the two remote interior angles. Here's how we can approach the problem step by step:
1. The exterior angle is (5x+9)°, and the remote interior angles are 33° and (2x)°.
2. According to the exterior angle theorem, the exterior angle is equal to the sum of the two remote interior angles. In this case:
(5x+9) = 33 + 2x
3. Now, we need to solve the equation to find the value of x:
5x + 9 = 33 + 2x
5x - 2x = 33 - 9
3x = 24
x = 24/3
x = 8
Therefore, the value of x in this problem is 8. By substituting x = 8 back into the equation, you can verify that it satisfies the condition for the triangle with the given exterior angle and interior angles.
Hope this helps you!
