{"@context":"https://schema.org/","@type":"Quiz","name":"

The measure of angle $R$ is $\\frac{2\\pi}{3}$ radians. The measure of angle $T$ is $\\frac{5\\pi}{12}$ radians greater than the measure of angle $R$. What is the measure of angle $T$, in degrees?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-geometry-and-trigonometry-multiple-choice-question-35"}],"about":{"@type":"Thing","name":"Math, Geometry and Trigonometry, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Geometry and Trigonometry","Duplicate"],"name":"

The measure of angle $R$ is $\\frac{2\\pi}{3}$ radians. The measure of angle $T$ is $\\frac{5\\pi}{12}$ radians greater than the measure of angle $R$. What is the measure of angle $T$, in degrees?

","comment":{"@type":"Comment","text":"

Choice C is correct. It's given that the measure of angle $R$ is $\\frac{2\\pi}{3}$ radians, and the measure of angle $T$ is $\\frac{5\\pi}{12}$ radians greater than the measure of angle $R$. Therefore, the measure of angle $T$ is equal to $\\frac{2\\pi}{3}+\\frac{5\\pi}{12}$ radians. Multiplying $\\frac{2\\pi}{3}$ by $\\frac{4}{4}$ to get a common denominator with $\\frac{5\\pi}{12}$ yields $\\frac{8\\pi}{12}$. Therefore, $\\frac{2\\pi}{3}+\\frac{5\\pi}{12}$ is equivalent to $\\frac{8\\pi}{12}+\\frac{5\\pi}{12}$, or $\\frac{13\\pi}{12}$. Therefore, the measure of angle $T$ is $\\frac{13\\pi}{12}$ radians. The measure of angle $T$, in degrees, can be found by multiplying its measure, in radians, by $\\frac{180}{\\pi}$. This yields $\\frac{13\\pi}{12}\\times\\frac{180}{\\pi}$, which is equivalent to 195 degrees. Therefore, the measure of angle $T$ is 195 degrees.

Choice A is incorrect. This is the number of degrees that the measure of angle $T$ is greater than the measure of angle $R$.

Choice B is incorrect. This is the measure of angle $R$, in degrees.

Choice D is incorrect and may result from conceptual or calculation errors.

"},"encodingFormat":"text/markdown","text":"

The measure of angle $R$ is $\\frac{2\\pi}{3}$ radians. The measure of angle $T$ is $\\frac{5\\pi}{12}$ radians greater than the measure of angle $R$. What is the measure of angle $T$, in degrees?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

120

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

390

"}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

195

","comment":{"@type":"Comment","text":"

"},"answerExplanation":{"@type":"Comment","text":"

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-geometry-and-trigonometry-multiple-choice-question-35"}

The measure of angle $R$ is $\frac{2\pi}{3}$ radians. The measure of angle $T$ is $\frac{5\pi}{12}$ radians greater than the measure of angle $R$. What is the measure of angle $T$, in degrees?