# Just one question – Calculate Angles

by Urwa
(Makkah)

Geometry – Calculate Angles

Lines PQ and RS intersect at point O.

∠POS = 4/5 * ∠ POR

Calculate the measures of ∠QOR and ∠QOS

### Comments for Just one question – Calculate Angles

 Aug 02, 2012 Calculate Angles by: Staff Answer: The sum of all four angles formed by the intersection of the two lines must = 360° ∠POS + ∠POR + ∠QOR + ∠QOS = 360° ∠POS and ∠QOR are vertical angles. Therefore, ∠POS = ∠QOR ∠POR and ∠QOS are also vertical angles. Therefore, ∠POR = ∠QOS At this point, the following information is known: ∠POS = ∠QOR ∠POR = ∠QOS ∠POS + ∠POR + ∠QOR + ∠QOS = 360° ∠POS = 4/5 * ∠ POR Using Substitution, rewrite the following equation so that it contains the single variable ∠ POR. ∠POS + ∠POR + ∠QOR + ∠QOS = 360° Substitute ∠POS for ∠QOR ∠POS + ∠POR + ∠POS + ∠QOS = 360° Substitute ∠POR for ∠QOS ∠POS + ∠POR + ∠POS + ∠POR = 360° Substitute (4/5 * ∠ POR) for ∠POS ∠POS + ∠POR + ∠POS + ∠POR = 360° 4/5 * ∠ POR + ∠POR + 4/5 * ∠ POR + ∠ POR = 360° Solve for ∠ POR using algebra 4/5 * ∠ POR + ∠POR + 4/5 * ∠ POR + ∠ POR = 360° (4/5 + 1 + 4/5 + 1) * ∠POR = 360° (4/5 + 4/5 + 1 + 1) * ∠POR = 360° (8/5 + 2) * ∠POR = 360° (1 + 3/5 + 2) * ∠POR = 360° (3 3/5) * ∠POR = 360° (3.6) * ∠POR = 360° (3.6) * ∠POR / 3.6 = 360° / 3.6 ∠POR * (3.6 / 3.6) = 360° / 3.6 ∠POR * (1) = 360° / 3.6 ∠POR = 360° / 3.6 ∠POR = 100° ∠POR = ∠QOS Therefore, ∠QOS = 100° ∠POS = 4/5 * ∠ POR ∠POS = 4/5 * 100° ∠POS = 80° ∠QOR = ∠POS Therefore, ∠QOR = 80° >>> The four angles are: ∠POR = 100° ∠QOR = 80° ∠QOS = 100° ∠POS = 80° Thanks for writing. Staff www.solving-math-problems.com

 Aug 03, 2012 Thanks sir/madam by: Anonymous Thank you v.v.v.v.v.v.vmuch