The different of the two angles in degree measure is $1$ and their sum in radian measure is also $1$ . What are the angles in circular measure?

(\frac{1}{2} - \frac{π}{360}), (\frac{1}{2} + \frac{π}{360})

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(\frac{1}{2} - \frac{90}{π}), (\frac{1}{2} + \frac{90}{π})

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(\frac{1}{2} - \frac{π}{180}), (\frac{1}{2} + \frac{π}{180})

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Solution

The correct option is B $(\frac{1}{2} - \frac{π}{360}), (\frac{1}{2} + \frac{π}{360})$
let angles be $θ_{1}$ and $θ_{2}$
we know that ,
( $1^{o}$ = $\frac{π}{180}$ radians)
Here, radian is circular measure of angle,
therefore,
$θ_{1} - θ_{2} = \frac{π}{180}$ ..............(1)
and,

$θ_{1} + θ_{2} = 1$ .............(2)
from equation (1) and (2),
$θ_{1} = \frac{1}{2} + \frac{π}{360}$
$θ_{2} = \frac{1}{2} - \frac{π}{360}$

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Similar questions

The circular measures of two angles of a triangle are 1/2 and 1/3.Find the third angle in degree measure.Take π= 22/7

How many of the following are matched correctly?

Degree measurement Radian measurement

(A) $180^{\circ}$ (1) $π$
(B) $60^{\circ}$ (2) $\frac{π}{6}$
(C) $0^{\circ}$ (3) 0
(D) $120^{\circ}$ (4) $\frac{2 π}{6}$
(E) $360^{\circ}$ (5) $2 π$
(F) $30^{\circ}$ (6) $\frac{π}{3}$
(G) $90^{\circ}$ (7) $\frac{π}{2}$
(H) $45^{\circ}$ (8) $\frac{π}{4}$
(I) $270^{\circ}$ (9) $3 π$

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The different of the two angles in degree measure is 1 and their sum in radian measure is also 1. What are the angles in circular measure?

The correct option is B (12−π360),(12+π360)let angles be θ1 and θ2we know that ,( 1o= π180 radians) Here, radian is circular measure of angle,therefore,θ1−θ2=π180 ..............(1)and, θ1+θ2=1 .............(2)from equation (1) and (2),θ1=12+π360θ2=12−π360

The different of the two angles in degree measure is $1$ and their sum in radian measure is also $1$ . What are the angles in circular measure?