Question

If possible please explain steps


Thank you!

Answer 1

They are equal to each other there for

6x -19 = 3x+32
6x-3x = 32+19
3x= 51
X= 51 divided by 3
X = 17

Angle 1 equals 180-83 =97
97 degrees

Answer 2

x = 17

m∠1 = 97°

Explanation:

According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.

Therefore, to find the value of x, we can set the expressions for the two given vertical angles equal to each other, and solve for x:

`\begin{aligned}(6x - 19)^(\circ) &= (3x + 32)^(\circ)\\6x-19&=3x+32\\6x-19-3x&=3x+32-3x\\3x-19&=32\\3x-19+19&=32+19\\3x&=51\\3x / 3&=51 / 3\\x&=17\end{aligned}`

Therefore, the value of x is 17.

Angles on a straight line sum to 180°.

Therefore, set the sum of m∠1 and the expression of one of its supplementary angles to 180°, substitute the found value of x, and solve for m∠1:

`\begin{aligned}m \angle 1+(3x+32)^(\circ)&=180^(\circ)\\m \angle 1+(3(17)+32)^(\circ)&=180^(\circ)\\m \angle 1+(51+32)^(\circ)&=180^(\circ)\\m \angle 1+83^(\circ)&=180^(\circ)\\m \angle 1+83^(\circ)-83^(\circ)&=180^(\circ)-83^(\circ)\\m \angle 1&=97^(\circ)\end{aligned}`

Therefore, the measure of angle 1 is 97°.