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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

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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

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