Answer:
[tex]m<R=87\°[/tex]
[tex]m<Q=93\°[/tex]
Step-by-step explanation:
we have that
[tex]m<R=(8x-1)\°[/tex]
[tex]m<Q=(9x-6)\°[/tex]
[tex]m<R+m<Q=180\°[/tex] ------> by supplementary angles
Substitute the values and solve for x
[tex]8x-1+9x-6=180\°[/tex]
[tex]17x-7=180\°[/tex]
[tex]17x=187\°[/tex]
[tex]x=11\°[/tex]
Find the value of angle R
[tex]m<R=(8*11-1)\°=87\°[/tex]
Find the value of angle Q
[tex]m<Q=(9*11-6)\°=93\°[/tex]
The measure of angle Q and R can be obtained by supplementary angle. The supplementary angle is defined as the addition of two angle is [tex]180^{\circ}[/tex].
The angle Q is [tex]93^{\circ}[/tex] and angle R is [tex]87^{\circ}[/tex].
Given:
The equation for unknown angle is,
[tex]8x -1 + 9x - 6 = 180[/tex]
The supplementary angle is,
[tex]\angle R+\angle Q=180^{\circ}[/tex]
Compare the above equation.
[tex]\angle R=(8x-1)^{\circ}\\\angle Q=(9x-6)^{\circ}[/tex]
Solve the given expression.
[tex]\begin{aligned}8x -1 + 9x -6 &= 180\\ 17x - 7 &= 180 \\17x &= 187 \\x&=11\\\end[/tex]
Calculate the Angle R.
[tex]\angle R=(8\times 11-1)\\\angle R=87^{\circ}[/tex]
Calculate the Angle Q.
[tex]\angle Q=(9\times 11-6)\\\angle Q=93^{\circ}[/tex]
Thus, the angle Q is [tex]93^{\circ}[/tex] and angle R is [tex]87^{\circ}[/tex].
Learn more about supplementary angle is here:
https://brainly.com/question/15613251
