Angles 1 and 2 are supplementary angles. The measure of angle 1 is given by $m\angle 1 = (2x-4)^\circ$ and the measure of angle 2 is given by $m\angle 2 = (4x-14)^\circ$. We need to find the measure of angle 1.

1. Problem Description

Angles 1 and 2 are supplementary angles. The measure of angle 1 is given by $m\angle 1 = (2x-4)^\circ$ and the measure of angle 2 is given by $m\angle 2 = (4x-14)^\circ$. We need to find the measure of angle

1.

2. Solution Steps

Since angles 1 and 2 are supplementary, their measures add up to 180 degrees.

$$m\angle 1 + m\angle 2 = 180^\circ$$

Substituting the given expressions for the measures of the angles, we get:

$$(2x - 4) + (4x - 14) = 180$$

Combining like terms, we have:

$$6x - 18 = 180$$

Adding 18 to both sides of the equation:

$$6x = 198$$

Dividing both sides by 6:

$$x = \frac{198}{6} = 33$$

Now, we can find the measure of angle 1 by substituting the value of $x$ into the expression for $m\angle 1$:

$$m\angle 1 = (2x - 4)$$

$$m\angle 1 = (2(33) - 4)$$

$$m\angle 1 = (66 - 4)$$

$$m\angle 1 = 62$$

Therefore, the measure of angle 1 is 62 degrees.

3. Final Answer

The measure of angle 1 is 62 degrees.