Solve the problem using the elimination method.
-Two angles are supplementary, and one is 5° more than six times the other. Find the larger angle.
A)155°
B)110°
C)25°
D)70°

Question

Quizplus · Accepted Answer

Let x be the smaller angle.
Then the larger angle is 6x + 5.
The sum of two supplementary angles is 180°.
So, we have the equation:
x + (6x + 5) = 180
Simplifying the equation, we get:
7x + 5 = 180
Subtracting 5 from both sides, we get:
7x = 175
Dividing both sides by 7, we get:
x = 25
Therefore, the larger angle is:
6x + 5 = 6(25) + 5 = 155.
Hence, the correct answer is A)155°. Let x be the smaller angle. The larger angle is then 6x + 5. According to the problem, these two angles are supplementary, so we know that:

x + 6x + 5 = 180

Simplifying this equation, we get:

7x + 5 = 180

Subtracting 5 from both sides, we get:

7x = 175

Dividing by 7, we get:

x = 25

So the smaller angle is 25 degrees. The larger angle is then:

6x + 5 = 6(25) + 5 = 155

Therefore, the larger angle is 155 degrees, which is choice A.

Solve the Problem Using the Elimination Method