Since ∠A and ∠B are vertical angles, they have equal measures. So, m∠A = m∠B.
Also, ∠B is a complementary angle with ∠C, meaning the sum of their measures is 90°. So, m∠B + m∠C = 90°.
Given that m∠A = 22°, we can substitute this value into the first equation. Therefore, m∠B = m∠A = 22°.
Substituting the value of m∠B into the second equation, we have:
22° + m∠C = 90°
This equation can be used to solve for m∠C.
In a diagram, ∠A and ∠B are vertical angles and ∠B is a complementary angle with ∠C. If m∠A = 22°, write a equation that you can use to solve for m∠C
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explain
Sure!
In the given diagram, ∠A and ∠B are shown as vertical angles, which means they share the same vertex and are opposite each other. One important property of vertical angles is that they have equal measures. So, we can say that m∠A = m∠B.
In addition, it is mentioned that ∠B is a complementary angle with ∠C. Complementary angles are two angles whose measures add up to 90°. In other words, if ∠B is one of the angles, ∠C is the other angle that, when combined with ∠B, makes a total of 90°. Mathematically, this can be represented as m∠B + m∠C = 90°.
Given that m∠A is known to be 22°, we can substitute this value into the first equation, so we have m∠B = 22°.
Now, we substitute the value of m∠B into the second equation, so we get:
m∠B + m∠C = 22° + m∠C = 90°
This equation shows that if we add the measure of ∠B (which is 22°) to the measure of ∠C, the sum will be 90°. We can use this equation to solve for the measure of ∠C by isolating the variable on one side of the equation.
In the given diagram, ∠A and ∠B are shown as vertical angles, which means they share the same vertex and are opposite each other. One important property of vertical angles is that they have equal measures. So, we can say that m∠A = m∠B.
In addition, it is mentioned that ∠B is a complementary angle with ∠C. Complementary angles are two angles whose measures add up to 90°. In other words, if ∠B is one of the angles, ∠C is the other angle that, when combined with ∠B, makes a total of 90°. Mathematically, this can be represented as m∠B + m∠C = 90°.
Given that m∠A is known to be 22°, we can substitute this value into the first equation, so we have m∠B = 22°.
Now, we substitute the value of m∠B into the second equation, so we get:
m∠B + m∠C = 22° + m∠C = 90°
This equation shows that if we add the measure of ∠B (which is 22°) to the measure of ∠C, the sum will be 90°. We can use this equation to solve for the measure of ∠C by isolating the variable on one side of the equation.
1 answer