Question

7. TOWERS A lookout tower sits on a network of struts and posts. Leslie measured two angles on the tower. If m∠1=7x-7°, m∠2=4x+2°, and m∠3=2x+6°, what is m∠1?

Answer 1

The angles in a triangle add up to 180 degrees

The measure of $\mathbf{\angle 1 }$ is $\frac{1162}{13}$

The given parameters are:

$\mathbf{\angle 1 = 7x - 7}$

$\mathbf{\angle 2 = 4x + 2}$

$\mathbf{\angle 3 = 2x + 6}$

The angles form a triangle.

So, we have:

$\mathbf{\angle 1 + \angle 2 + \angle 3 = 180}$

This gives

$\mathbf{7x - 7 + 4x + 2 + 2x + 6 = 180}$

Collect like terms

$\mathbf{7x + 4x + 2x = 180 + 7 - 2 - 6}$

$\mathbf{13x = 179}$

Divide by 13

$\mathbf{x = \frac{179}{13}}$

Substitute $\mathbf{x = \frac{179}{13}}$ in $\mathbf{\angle 1 = 7x - 7}$

So, we have:

$\mathbf{\angle 1 = 7 \times \frac{179}{13} - 7}$

$\mathbf{\angle 1 = \frac{1253}{13} - 7}$

So, we have:

$\mathbf{\angle 1 = \frac{1253 - 13 \times 7}{13}}$

$\mathbf{\angle 1 = \frac{1162}{13}}$

Hence, the measure of $\mathbf{\angle 1 }$ is $\frac{1162}{13}$

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