Question

6. The sum of the measures of two angles is 100° and
2
their difference is find the measures of the angles
9
in radians.​

Answer 1

Answer:

I don't know sorry sis sorry

Answer 2

Answer:

The measure of the two angles in radians are $\frac{7}{18} \pi$ radians,  $\frac{1}{6} \pi$ radians

Explanation:

In the given problem the difference between the measure of angles is might be 2$\pi$/9

Given that sum of the measures of two angles = 100°

                 difference between the two angles = 2$\pi$/9  

       $\pi$ =180 ⇒ 2$\pi$/9    ⇒ 2(180)/9

                                    ⇒ 40°              

here we need to find measure of the angles in radians

let the two angles are $a$ and $b$  

sum of the measure of angles ⇒ $a + b = 100$ _(1)  

difference of measure of angles ⇒ $a-b = 40$ _(2)

add (1) and (2) ⇒  $a+ b+a-b =$ 100° + 40°  

                       ⇒ 2 $a$ =140°

                       ⇒ $a$ =140/2 = 70°  

substitute $a$ = 70° in (1) ⇒  70° + $b$ = 100°

                                     ⇒ b =100°-70°

                                     ⇒ b = 30°

the measure of the both angles are  70° and 30°

now we need to convert both values into radians

To convert degrees into radians multiply with $\pi$/ 180

                    70° ⇒ 70° × $\frac{\pi }{180}$ =  $\frac{7}{18}\pi$ radians

                    30° ⇒ 30° × $\frac{\pi }{180}$ = $\frac{1}{6} \pi$ radians