Parallel Lines and Angle Calculation

MathematicsGeometry - Angles in Parallel LinesMediumLGS

Published:

12-

$$d_1 // d_2$$

$$\alpha = ?$$

(The figure shows two parallel lines $d_1$ and $d_2$. There are angles formed by segments. At the top line $d_1$, an angle is bisected (marked with double ticks). At the bottom line $d_2$, another angle is bisected (marked with dots). An intermediate angle is $40^\circ$ and the target angle is $\alpha$.)

This question includes visual content: The image shows two horizontal parallel lines labeled d1 and d2. Between these lines, there are two sets of broken lines forming zigzag patterns. The leftmost vertex of the first pattern is labeled 40 degrees. There are two angle bisector markings on the upper line d1 and two different angle bisector markings (dots) on the lower line d2. A second vertex pointed towards the right is labeled with the Greek letter alpha. A text on the right states d1 // d2 and asks for alpha = ?.

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Step by Step Written Solution

1
Step 1

Merhaba! Bu geometri probleminde, birbirine paralel de bir ve de iki doğruları arasına çizilmiş açılarla ilgili bir soru çözeceğiz. Amacımız alfa açısını bulmak.

Paralel Doğrularda Açılar

2
Step 2

Şekle dikkatlice bakalım. de bir ve de iki doğruları paraleldir. Üstte ve altta açıortaylar verilmiş. Bu açıortayları isimlendirelim.

d1d240°α
3
Step 3

Üstteki açıortayın her bir parçasına x, alttaki açıortayın her bir parçasına y diyelim.

4
Step 4

Paralel doğrular arasında sola bakan açıların toplamı sağa bakan açıların toplamına eşittir. Biz buna 'M kuralı' veya 'Zikzak kuralı' diyoruz.

Zikzak (M) Kuralı

5
Step 5

Önce dıştaki daha geniş olan kırık çizgiye bakalım. Burada sağa bakan açılar x ve y, sola bakan ise kırk derecedir.

$$x + y = 40^\circ$$

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About This Question

Subject
Mathematics
Topic
Geometry - Angles in Parallel Lines
Difficulty
Medium
Exam
LGS
Question Type
Open Ended

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