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By properties of parallel lines and triangles, the measure of the angle RSP is equal to 49°.
In this problem we find a geometric system formed by two triangles. By alternating internal angles, the angles QRP and RPS are congruent. Thus:
5 · y + 14 = 8 · y - 13
3 · y = 27
y = 9
The sum of the measures of internal angles in triangles are always equal to 180°:
(8 · y - 13) + 3 · x + (2 · x + 1) = 180
8 · y + 5 · x - 12 = 180
8 · y + 5 · x = 192
5 · x = 192 - 8 · y
x = (192 - 8 · y) / 5
x = (192 - 8 · 9) / 5
x = 24
Lastly, the measure of the angle RSP is equal to:
m ∠ RSP = (2 · 24 + 1)
m ∠ RSP = 49°
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Rewritten by : Barada
When parallel lines are cut by a transversal, several angles are formed. These include corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. Understanding these angle relationships can help solve problems involving parallel lines and transversals.
When parallel lines are cut by a transversal, several angles are formed.
Understanding these angle relationships can help solve problems involving parallel lines and transversals.
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