Two lines are parallel and one transversal is intersecting them. If one pair of co-interior angles Are in the ratio 4:5 then, find the each of the angle of same pair.
when two lines are parallel and a transversal intersects them, co-interior angles are formed on the same side of the transversal. Let's say one pair of co-interior angles is in the ratio 4:5.
We can represent the angles as 4x and 5x, where x is a common factor. These angles are measured in degrees. So, if we let 4x be the smaller angle and 5x be the larger angle, we can find the value of x by adding the angles together and setting the sum equal to 180 degrees, since the sum of the co-interior angles is always 180 degrees.
So, 4x + 5x = 180. Combining like terms, we get 9x = 180. Dividing both sides by 9, we find that x = 20.
Now we can substitute the value of x back into the expressions for the angles:
Smaller angle = 4x = 4 × 20 = 80 degrees
Larger angle = 5x = 5 × 20 = 100 degrees
Therefore, the smaller angle of the pair is 80 degrees, and the larger angle is 100 degrees.
Answers & Comments
Answer:
Let the angles be 3x and 7x.
Let the angles be 3x and 7x.We know that sum of two interior angles on the same side of transversal is 180 ∘ .
3x+7x=180 ∘
3x+7x=180 ∘ ⇒10x=180 ∘
⇒x=18 ∘
⇒x=18 ∘ Therefore, the greater angle is 7x=7×18=126∘
Verified answer
Step-by-step explanation:
when two lines are parallel and a transversal intersects them, co-interior angles are formed on the same side of the transversal. Let's say one pair of co-interior angles is in the ratio 4:5.
We can represent the angles as 4x and 5x, where x is a common factor. These angles are measured in degrees. So, if we let 4x be the smaller angle and 5x be the larger angle, we can find the value of x by adding the angles together and setting the sum equal to 180 degrees, since the sum of the co-interior angles is always 180 degrees.
So, 4x + 5x = 180. Combining like terms, we get 9x = 180. Dividing both sides by 9, we find that x = 20.
Now we can substitute the value of x back into the expressions for the angles:
Smaller angle = 4x = 4 × 20 = 80 degrees
Larger angle = 5x = 5 × 20 = 100 degrees
Therefore, the smaller angle of the pair is 80 degrees, and the larger angle is 100 degrees.
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