In the figure below, line m is perpendicular to line n and both lines intersect line q at the same point. The measure of ∠1 is (3x - 10)°, and the measure of ∠2 is (2x + 10)°. What is the measure of ∠3 ?
Question
In the figure below, line m is perpendicular to line n and both lines intersect line q at the same point. The measure of ∠1 is (3x - 10)°, and the measure of ∠2 is (2x + 10)°. What is the measure of ∠3 ?
Solution
The problem doesn't provide a figure, but based on the description, we can infer that ∠1 and ∠2 are adjacent angles on line q, which means they are supplementary. Therefore, their measures add up to 180°.
So, we can set up the equation (3x - 10) + (2x + 10) = 180.
Solving this equation:
5x = 180 x = 36
Now, since line m is perpendicular to line n, ∠3 is a right angle, which means it measures 90°.
Similar Questions
The intersection of lines l and m forms the 4 angles ∠𝐴, ∠𝐵, ∠𝐶 𝑎𝑛𝑑 ∠𝐷, and . The measure of ∠𝐵 is 312 times the measure of ∠𝐴 . Which of the following values is closest to the measure of ∠𝐴 ?
Lines p and q are perpendicular. If the slope of line p is 2, what is the slope of line q?A.-2B.2C.D.-
n given Figure Pq parallel rs and l IA transversal intersecting pq and rs at a and b respectively ta and to are bisectors of angle qab and angle sba respectively find the measure of angle atb
In the figure below, 𝐴𝐵― is parallel to 𝐷𝐸―, the measure of ∠𝐴𝐵𝐶 is 49°, and the measure of ∠𝐵𝐶𝐷 is 137°. What is the measure of ∠𝐶𝐷𝐸 ?
In a plane, the distinct lines 𝐴𝐵↔ and 𝐶𝐷↔ intersect at A, where A is between C and D. The measure of ∠𝐵𝐴𝐶 is 54∘. What is the measure of ∠𝐵𝐴𝐷 .
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.