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In the given figure two straight lines AB and PQ intersect at a point O. If ∠AOC = 42° what is the measure of ∠BOD?
- a)42°
- b)133°
- c)123°
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In the given figure two straight lines AB and PQ intersect at a point ...
It is because they are vertically opposite to each other.The rule is also that vertically opposite angles are equal. So its is 47 degerees
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Community Answer
In the given figure two straight lines AB and PQ intersect at a point ...
We can solve the problem using the properties of alternate interior angles and the fact that the sum of angles in a triangle is 180 degrees.
First, we notice that angles AOB and POQ are alternate interior angles, which means they are equal. Therefore, we can write:
angle AOB = angle POQ = x (1)
Similarly, angles AOP and BOQ are also alternate interior angles and are therefore equal. We can write:
angle AOP = angle BOQ = y (2)
Now, let's consider triangle AOB. The sum of angles in a triangle is 180 degrees, so we can write:
angle AOB + angle ABO + angle BAO = 180
Substituting (1) and (2) into this equation, we get:
x + (180 - 2y) + (180 - 2x) = 180
Simplifying this equation, we get:
-x - 2y = -180 (3)
Similarly, we can consider triangle OPQ and write:
angle POQ + angle OPQ + angle OQP = 180
Substituting (1) and (2) into this equation, we get:
x + y + (180 - 2x - 2y) = 180
Simplifying this equation, we get:
-x - y = -90 (4)
Now we have two equations (3) and (4) with two unknowns (x and y). We can solve for one variable in terms of the other using either equation, and then substitute that expression into the other equation to get a single equation in one variable. For example, we could solve equation (3) for x:
x = 2y - 180
Substituting this into equation (4), we get:
-(2y - 180) - y = -90
Simplifying this equation, we get:
y = 45
Now we can substitute this value of y into equation (3) to get:
x = 135
Therefore, the angles AOB and POQ are both 135 degrees, and the angles AOP and BOQ are both 45 degrees.
First, we notice that angles AOB and POQ are alternate interior angles, which means they are equal. Therefore, we can write:
angle AOB = angle POQ = x (1)
Similarly, angles AOP and BOQ are also alternate interior angles and are therefore equal. We can write:
angle AOP = angle BOQ = y (2)
Now, let's consider triangle AOB. The sum of angles in a triangle is 180 degrees, so we can write:
angle AOB + angle ABO + angle BAO = 180
Substituting (1) and (2) into this equation, we get:
x + (180 - 2y) + (180 - 2x) = 180
Simplifying this equation, we get:
-x - 2y = -180 (3)
Similarly, we can consider triangle OPQ and write:
angle POQ + angle OPQ + angle OQP = 180
Substituting (1) and (2) into this equation, we get:
x + y + (180 - 2x - 2y) = 180
Simplifying this equation, we get:
-x - y = -90 (4)
Now we have two equations (3) and (4) with two unknowns (x and y). We can solve for one variable in terms of the other using either equation, and then substitute that expression into the other equation to get a single equation in one variable. For example, we could solve equation (3) for x:
x = 2y - 180
Substituting this into equation (4), we get:
-(2y - 180) - y = -90
Simplifying this equation, we get:
y = 45
Now we can substitute this value of y into equation (3) to get:
x = 135
Therefore, the angles AOB and POQ are both 135 degrees, and the angles AOP and BOQ are both 45 degrees.
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In the given figure two straight lines AB and PQ intersect at a point O. If ∠AOC = 42° what is the measure of ∠BOD?a)42°b)133°c)123°d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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