Question

HELPPPPPPPP!!!!

Angles ABC and DBE are vertical angles where m∠ABC = (7x + 7)° and m∠DBE = (8x − 4)°.

Part A: Solve for x. Show every step of your work.

Part B: Are the vertical angles also supplementary angles? Explain.

Answer 1

We solve for x by setting the expressions for the vertical angles equal and find x = 11°. Vertical angles are congruent but not necessarily supplementary.

Step-by-step explanation:

To solve for x when given that angles ABC and DBE are vertical angles, we use the property that vertical angles are congruent. Therefore, we set the expressions for m∠ABC and m∠DBE equal to each other and solve for x:

1. Set the expressions equal: (7x + 7)° = (8x − 4)°.
2. Subtract 7x from both sides: 7° = x − 4°.
3. Add 4° to both sides to solve for x: x = 11°.

For Part B, vertical angles are not necessarily supplementary angles; they are congruent. Supplementary angles add up to 180°, while vertical angles are equal in measure because they are opposite angles formed by the intersection of two straight lines.

Answer 2

Part A:

To solve for x, we can set the measures of the vertical angles equal to each other and solve the resulting equation.

Given:

m∠ABC = (7x + 7)°

m∠DBE = (8x − 4)°

Since angles ABC and DBE are vertical angles, they have equal measures. Therefore, we can set up the equation:

7x + 7 = 8x - 4

Now, let's solve for x:

7x - 8x = -4 - 7

-x = -11

x = 11

So, x equals 11.

Part B:

Vertical angles are always congruent, meaning they have the same measure. However, the term "supplementary angles" refers to a pair of angles whose measures add up to 180 degrees.

Since vertical angles have equal measures, they are not always supplementary angles unless their measures add up to 180 degrees. In this case, we have:

m∠ABC = (7x + 7)° = (7(11) + 7)° = 84°

m∠DBE = (8x − 4)° = (8(11) − 4)° = 84°

Since the measures of both angles are 84 degrees, they are congruent but not supplementary.

Therefore, the vertical angles in this scenario are not supplementary angles.

Step-by-step explanation: