.) If a transversal intersects two parallel lines such that the ratio between the interior angles on one of its side is is 3 : 7 , then the measure of the smaller angle is _____°.
1 point
54
126
30
70
Answers
Answer:
54 is the measure of the smaller angle
Explanation:
3x+7x=180°
10x=180°
x=18°
now,3x=3×18°=54°
7x=7×18°=126°
so smaller angle = 54°
Given : a transversal intersects two parallel lines such that the ratio between the interior angles on one of its side is is 3 : 7
To Find : the measure of the smaller angle is _____°
Solution:
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent.
• Alternate angles are congruent. ( Interiors & Exterior both )
• Interior angles are supplementary. ( adds up to 180°)
Let say interior angles are 3k & 7k
3k + 7k = 10k
10k = 180
=> k = 18
3k is smaller than 7k
3k = 3 * 18 = 54
the measure of the smaller angle is 54°
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