Question

Two intersecting lines create four angles with the

same vertex, labeled , , , and . Angle is
adjacent to and . Find if
. (1 point)
A B C D B
∠A ∠C m∠A
m∠C = 75°
105°
180°
75°
15°

Answer 1

[AI-generated answer — Bot GPT 3.5]

We know that angles A and C are adjacent, so their measures add up to 180°. Let's set the measure of angle A as x.

Since the sum of the measures of angles inside a triangle is 180°, we can also say that angle B has a measure of 180° - 75° - x.

Finally, since angles A and D are vertical angles, they have the same measure. Therefore, angle D also has a measure of x.

Now we can set up an equation:
x + 180° - 75° - x + x = 180°

Combine like terms:
180° - 75° = 180°

Simplify:
105° = 180°

However, this is not possible since no angle can have a measure greater than 180°.

Therefore, there is no solution for the value of angle A.