Question
Two angles are supplementary with measures m∠QRS=(x+30)° and m∠SRT=(2x)°. What is the value of m∠QRS?(1 point)
Answers
Answer
Four angles share a vertex. They have the following measures: m∠1=63°, m∠2=117°, m∠3=63°, and m∠4=117°. Which angle is a vertical angle with ∠2?
Answered by
GPT 3.5
Since the angles QRS and SRT are supplementary, the sum of their measures is 180 degrees.
Therefore, we can write the equation: (x+30) + (2x) = 180
Combining like terms: 3x + 30 = 180
Subtracting 30 from both sides: 3x = 150
Dividing both sides by 3: x = 50
Therefore, the measure of angle QRS is (x+30) = (50+30) = 80 degrees. Answer: \boxed{80}.
Therefore, we can write the equation: (x+30) + (2x) = 180
Combining like terms: 3x + 30 = 180
Subtracting 30 from both sides: 3x = 150
Dividing both sides by 3: x = 50
Therefore, the measure of angle QRS is (x+30) = (50+30) = 80 degrees. Answer: \boxed{80}.
Answered by
GPT 3.5
Vertical angles are formed by two intersecting lines and are congruent (equal in measure).
Given that ∠2 = 117°, the vertical angle to ∠2 would have the same measure.
Looking at the given measures, ∠1 = 63° and ∠3 = 63°, but ∠1 is not congruent to ∠2.
Therefore, the vertical angle to ∠2 is ∠4.
Answer: ∠4
Given that ∠2 = 117°, the vertical angle to ∠2 would have the same measure.
Looking at the given measures, ∠1 = 63° and ∠3 = 63°, but ∠1 is not congruent to ∠2.
Therefore, the vertical angle to ∠2 is ∠4.
Answer: ∠4