Question

<1 and <2 form a linear pair. The <1 is 75 less than 5 times the <2. What is the measure of <1?

A) 45°
B) 50°
C) 115°
D) 959°

Answer 1

Angle 1 is 137.5 degrees.

Step-by-step explanation:

Let's assume that angle 1 = x degrees and angle 2 = y degrees.

We know that angle 1 is 75 degrees less than 5 times angle 2:

x = 5y - 75

Since angles 1 and 2 form a linear pair, they add up to 180 degrees:

x + y = 180

Now we can solve this system of equations:

Substitute the value of x from the first equation into the second equation:

(5y - 75) + y = 180

Combine like terms:

6y - 75 = 180

Add 75 to both sides:

6y = 255

Divide by 6:

y = 42.5

Substitute this value back into the first equation:

x = 5(42.5) - 75

x = 212.5 - 75

x = 137.5

So the measure of angle 1 is 137.5 degrees.