Question

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.

Answer 1

148º

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