Question

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

Answer 1

Answer:

$\angle QRT=125.6\°$

$\angle RTQ=6.4\°$

$\angle TQR=48\°$

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 $17x$ is an exterior angle of the triangle QRT. Then:

$17x=\angle RTQ+\angle TQR$

Where:

$\angle RTQ=2x\\\\\angle TQR=48\°$

Substituting values and solving for "x", we get:

$17x=2x+48\\\\17x-2x=48\\\\15x=48\\\\x=3.2$

Then:

$17x=17(3.2)=54.4\°\\\\\\\angle RTQ=2(3.2)=6.4\°$

The sum of the interior angles of a triangle is 180°, therefore:

$\angle QRT+\angle RTQ+\angle TQR=180$

Solving for $\angle QRT$, we get:

$\angle QRT=180-48-6.4=125.6\°$