Answer:
x = 25
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180°.
The measure of two angles is given as 55 and 75, then, the measure of the missing angle can be calculated as follows:
55 + 75 + 2x = 180
130 + 2x = 180
2x = 50
x = 25
Final answer:
To find the value of x for the third angle of a triangle when given two angles, we use the triangle sum theorem, set up the equation 55 + 75 + 2x = 180, and solve for x, which results in x being 25. Therefore , the correct answer options is a)
Explanation:
The question involves finding the value of x when given the three angles of a triangle with measures 55, 75, and 2x. According to the triangle sum theorem, the sum of the interior angles in a triangle is 180 degrees. We set up the equation 55 + 75 + 2x = 180 and solve for x.
To solve the equation, we first combine the known angles: 55 + 75 = 130. Then subtract this sum from 180 to find the measure of the third angle: 180 - 130 = 50. The third angle is 2x, so we set up the equation 2x = 50. Dividing both sides by 2, we find that: x = 25.
Therefore, the correct answer is (a) 25.
