Final answer:
To solve for x in this problem, set up an equation using the angles of a triangle. The third angle is found by subtracting the sum of the given angles from 180°. By setting up a proportion, x can be solved for by multiplying the known angle by 180° and dividing by the sum of the angles.
Step-by-step explanation:
To solve for x in this problem, we can set up an equation using the angles of a triangle. The sum of the angles in a triangle is always 180°. We have one angle given as 49° and another angle given as 14°. To find the third angle, we subtract the sum of the given angles from 180°. Therefore, the third angle is 180° - 49° - 14° = 117°.
Since we now know the measures of all three angles in the triangle, we can determine the value of x by setting up a proportion. The ratio of the measure of an angle to the fraction of the total sum of the angles it represents is equal to the ratio of x to 180°. In this case, we have:
(49° / 117°) = (x / 180°)
Cross-multiplying, we find:
49° * 180° = 117° * x
Simplifying and solving for x, we get:
x = (49° * 180°) / 117° ≈ 75.24°
Therefore, the value of x is approximately 75.24°.
Learn more about Angles in a triangle