Since angle B is adjacent to both angle A and angle C, we can add the measures of angle A and angle C together to find the measure of angle B.
m∠B = m∠A + m∠C
Since m∠C = 75°, we can substitute this value into the equation.
m∠B = m∠A + 75
Since the sum of all angles at a vertex is 180°, we can write another equation.
m∠A + m∠B + m∠C + m∠D = 180
We can substitute the value of m∠C and simplify the equation.
m∠A + m∠B + 75 + m∠D = 180
We are given that the four angles all have the same vertex, so m∠A = m∠B, and m∠C = m∠D.
Substituting these values into the equation, we get:
2m∠A + 75 + 2m∠A = 180
4m∠A + 75 = 180
Subtracting 75 from both sides:
4m∠A = 105
Dividing both sides by 4:
m∠A = 26.25°
So the measure of angle A is 26.25°.
None of the given answer choices are correct, so it seems there may be a mistake in the question or the solutions provided.
Two intersecting lines create four angles with the same vertex, labeled A , B , C , and D . Angle B is adjacent to ∠A and ∠C . Find m∠A if m∠C=75° .(1 point)
75°
15°
105°
180°
3 answers
wrong
Apologies for the mistake. Let's reevaluate the problem.
Since angles A, B, C, and D are all formed by two intersecting lines, we know that angle A and angle C are vertical angles. Vertical angles are congruent, meaning they have the same measure.
Given that m∠C = 75°, we can conclude that m∠A = 75° as well.
Therefore, the correct answer is:
m∠A = 75°.
Since angles A, B, C, and D are all formed by two intersecting lines, we know that angle A and angle C are vertical angles. Vertical angles are congruent, meaning they have the same measure.
Given that m∠C = 75°, we can conclude that m∠A = 75° as well.
Therefore, the correct answer is:
m∠A = 75°.