In the diagram below, ST is parallel to QR. angle P is 40 degrees, and QST is 2R+8. Find the measure of STR in degrees.

Mathematics

1 answer:

lozanna [386]2 years ago

3 0

Answer:

148º

Step-by-step explanation:

Use the information given:

The measure of a straight line is 180º. So angle PST=180-(2R+8)
Since ST and QR are parallel, angle PST=angle PQR. Now, angle PQR=180-(2R+8)
The sum of a triangle's interior angles is 180º. So 40+180-2R-8+R=180º.
Combine like terms, 212-R=180
Subtract, -R=-32
Convert to positive, R=32º

With R=32º, we can find angle QST and PQR. Angle QST=2(32)+8=64+8=72º. So angle PQR=180º-72º=108º. The sum of a quadrilateral's interior angles is 360º:

32º+72º+108º+STR=360º
Combine like terms, 212º+STR=360º
Subtract, STR=148º

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