Answer:
x = 14
Explanation:
We can solve for x using the following steps:
Step 1: Find the measure of the angle beside the 35° angle (let's call it angle y):
- The 35° and angle y both lie on a straight line and are right beside each other, meaning that they are supplementary angles.
- This means that the sum of the two angles is 180°.
Thus, we can find the measure of angle y by subtracting 35 from 180:
(m∠y + 35 = 180) - 35
m∠y = 145°
Therefore, the measure of angle y is 145.
Step 2: Set the sum of 145, (x - 7) and 2x equal to 180:
- The triangle sum theorem says that the sum of a triangle's interior angles equals 180°.
Thus, we can solve for x by setting the sum of 145, (x - 7), and 2x equal to 180:
145 + x - 7 + 2x = 180
(145 - 7) + (x + 2x) = 180
(138 + 3x = 180) - 138
(3x = 42) / 3
x = 14
Therefore, x = 14.