Respuesta :
We know that the angles add up to 180° and we also know that one angle is 3° less than twice the other.
Now, we can represent the situation using a system of equations
[tex]\begin{cases}x+y=180^{\circ}\ldots(1) \\ 2y-3^{\circ}=x\ldots(2)\end{cases}[/tex]Where,
- x represents the measure of one angle
- y represents the measure of the second angle
Then, we must solve the sysyem of equations
1. we can multiply the first equation by -2
[tex]\begin{gathered} -2(x+y)=-2(180^{\circ}) \\ -2x-2y=-360^{\circ}\ldots(3) \end{gathered}[/tex]2. we can rewrite the equation (2) as
[tex]-x+2y=3^{\circ}[/tex]3. We must add up equations (2) and (3)
[tex]\begin{gathered} -x+2y=3^{\circ} \\ -2x-2y=-360^{\circ} \\ ------------- \\ -3x=-357^{\circ}\ldots(4) \end{gathered}[/tex]4. We can solve equation (4) for x
[tex]\begin{gathered} -3x=-357^{\circ} \\ x=\frac{-357^{\circ}}{-3} \\ x=119^{\circ} \end{gathered}[/tex]5. We must replace x = 119° in equation (1) and then we must solve for y
[tex]\begin{gathered} 119^{\circ}+y=180^{\circ} \\ y=180^{\circ}-119^{\circ} \\ y=61^{\circ} \end{gathered}[/tex]Finally, the measurements of the two angles are 119° and 61°
