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In the diagram [MN] is parallel to [PQ] - Junior Cycle Mathematics - Question 3(a) - 2012

Question 3(a)

In the diagram [MN] is parallel to [PQ]. ∠POQ = 43° and ∠QOP = 70°. Find (i) the value of $x$. (ii) the value of $y$.

Worked Solution & Example Answer:In the diagram [MN] is parallel to [PQ] - Junior Cycle Mathematics - Question 3(a) - 2012

Step 1

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Answer

To find the value of $x$ , we can use the fact that the sum of angles in triangle $MPO$ is equal to $180°$ :

$ext{Sum of angles} = ext{angle } MPO + ext{angle } POQ + ext{angle } OPQ = 180°$

Substituting the known values: $x + 43° + 70° = 180°$

Now, solve for $x$ : $x + 113° = 180°$ $x = 180° - 113°$ $x = 67°$

Thus, the value of $x$ is $67°$ .

Step 2

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Answer

To find the value of $y$ , we note that in triangle $QOP$ , the sum of the angles is also $180°$ :

$ext{Sum of angles} = ext{angle } OPQ + ext{angle } QOP + ext{angle } OQP = 180°$

Substituting the known values: $70° + 43° + y = 180°$

Now, solve for $y$ : $113° + y = 180°$ $y = 180° - 113°$ $y = 67°$

Thus, the value of $y$ is $67°$ .

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