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If $l_1 \parallel l_2$, find the sizes of the angles $\alpha$, $\beta$ and $\gamma$ in the following diagram - Junior Cycle Mathematics - Question 11 - 2013

Question 11

$If-$l_1-\parallel-l_2$,-find-the-sizes-of-the-angles-$\alpha$,-$\beta$-and-$\gamma$-in-the-following-diagram-Junior Cycle Mathematics-Question 11-2013.png$

If $l_1 \parallel l_2$, find the sizes of the angles $\alpha$, $\beta$ and $\gamma$ in the following diagram. ![Diagram](https://example.com/diagram)

Worked Solution & Example Answer:If $l_1 \parallel l_2$, find the sizes of the angles $\alpha$, $\beta$ and $\gamma$ in the following diagram - Junior Cycle Mathematics - Question 11 - 2013

Step 1

Find $\alpha$

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Answer

We consider the triangle with angles $73^\circ$ , $60^\circ$ , and $2\alpha$ . The sum of these three angles is $180^\circ$ :

$2\alpha + 73 + 60 = 180$

This simplifies to:

$2\alpha = 180 - 73 - 60 = 47$

Thus,

$\alpha = \frac{47}{2} = 23.5^\circ$

Step 2

Find $\beta$

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Answer

Next, we consider the triangle with angles $\alpha$ , $\beta$ , and $73^\circ$ . Again, the sum of these angles is $180^\circ$ :

$73 + \alpha + \beta = 180$

Substituting the value of $\alpha$ we calculated:

$73 + 23.5 + \beta = 180$

This simplifies to:

$\beta = 180 - 73 - 23.5 = 83.5^\circ$

Step 3

Find $\gamma$

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101 rated

Answer

Finally, since the two lines are parallel, corresponding angles are equal. Therefore:

$\gamma = \alpha = 23.5^\circ$

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