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°
75°
180°
15°
105°
Let's call the two intersecting lines AB and CD.
Since angle A is adjacent to angle B and angle C, we can conclude that angle A is the sum of angle B and angle C.
Therefore, m∠A = m∠B + m∠C.
We are given that m∠A = 75° and m∠C = 75°.
Since angle B and angle D are vertical angles, they are congruent. Therefore, m∠B = m∠D.
Since angle B and angle C are adjacent angles, they share the same vertex and one side. Therefore, they are supplementary angles. This means that m∠B + m∠C = 180°.
Substituting the given values, we have:
75° = m∠B + 75°
Simplifying the equation, we have:
75° - 75° = m∠B
0° = m∠B
Therefore, m∠B = 0°.
Since m∠B = m∠D, we can conclude that m∠D = 0°.
In conclusion, m∠D = 0°.
the answer is in the options
Apologies for not providing the answer in the options earlier. Let's check each option to see which one satisfies the given conditions:
Option 1: 75° - 75° = 0° (m∠B)
Option 2: 75° does not appear in the options
Option 3: 75° - 0° = 75° (m∠B)
Option 4: 75° + 0° = 75° (m∠B)
From the options, only option 1 (0°) and option 4 (75°) satisfy m∠B. Therefore, the answer is either 0° or 75°.