Question

Find the m< 1 if m< 1 =(5x)° and m<4= (2x +90)°.

Answer 1

150°

Explanation:

We can use angle relationships to solve for unknown measurements.

Vertical Angles

Vertical angles are pairs of opposite angles made from 2 intersecting lines. In this case, ∠1 and ∠4 are vertical angles because they are opposite of each other. All vertical angles are congruent. This means that ∠1 and ∠4 have equal measurements. Additionally, ∠2 and ∠3 are vertical angles.

Solving for ∠1

Since we know that ∠1 = ∠4, we can set their expressions equal to each other. Then, we can solve for x.

• 5x = 2x + 90

Then, subtract 2x from both sides.

• 3x = 90

Next, divide by 3.

• x = 30

Finally, plug in x for the original expression for ∠1.

• 5(30) = 150

So, ∠1 = 150 degrees.