We get x is 10°. So angle A is 50°, angle B is 46°, and angle C is 84°.
Step-by-step explanation:
Step 1:
The sum of all the angles for a straight line is 180°. So the sum of the three given angles is 180°.
The angles are [tex]6x-10^\circ[/tex], [tex]4x+6^\circ,[/tex] and [tex]7x+14^\circ.[/tex]
So [tex]6x -10 + 4x +6+7x +14 = 180.[/tex]
[tex]17x + 10 = 180.[/tex]
[tex]17x = 170, x = \frac{170}{17} = 10.[/tex]
So x = 10°.
Step 2:
Angle A[tex]= 6x - 10^\circ = 60 - 10 = 50^\circ.[/tex] Angle A is an acute angle.
Angle B [tex]= 4x+6^\circ = 40+6 =46^\circ.[/tex] Angle B is an acute angle.
Angle C [tex]= 7x + 14^\circ = 70 + 14= 84^\circ.[/tex] Angle C is also an acute angle.
