12. Find the measure of each interior angle of triangle QRT.

Accepted Solution

Answer: [tex]\angle QRT=125.6\°[/tex] [tex]\angle RTQ=6.4\°[/tex] [tex]\angle TQR=48\°[/tex] Step-by-step explanation: It is important to remember that, by definition, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. In this case we can idenfity that the angle [tex]17x[/tex] is an exterior angle of the triangle QRT. Then: [tex]17x=\angle RTQ+\angle TQR[/tex] Where: [tex]\angle RTQ=2x\\\\\angle TQR=48\°[/tex] Substituting values and solving for "x", we get: [tex]17x=2x+48\\\\17x-2x=48\\\\15x=48\\\\x=3.2[/tex] Then: [tex]17x=17(3.2)=54.4\°\\\\\\\angle RTQ=2(3.2)=6.4\°[/tex] The sum of the interior angles of a triangle is 180°, therefore: [tex]\angle QRT+\angle RTQ+\angle TQR=180[/tex] Solving for [tex]\angle QRT[/tex], we get: [tex]\angle QRT=180-48-6.4=125.6\°[/tex]