In Fig. 6.29, 1|m. Find the values of a, b, c and d. 30° a 32° >m
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Subject:
Math -
Author:
cindyjensen -
Created:
1 year ago
Answers 1
Answer:
x = 126°
Step-by-step explanation:
Given: AB || CD, CD || EF and y : z = 3 : 7
To find: The value of x
When two parallel lines are cut by a transversal, co-interior angles formed are supplementary.
Also, we know that lines which are parallel to the same line are parallel to each other.
Thus, If AB || CD, CD || EF, we can say AB || EF.
Therefore, the angles x and z are alternate interior angles and hence are equal.
x = z.......(1)
AB and CD are parallel lines cut by a transversal. So the co-interior angles formed are supplementary.
x + y = 180°.
Since x = z,
We get y + z = 180°......... (2)
Let, y = 3a, z = 7a [Since, y : z = 3 : 7]
Substituting the values in equation (2),
3a + 7a = 180°
10a = 180°
a = 180°/10
a = 18°
∴ y = 3a = 3 × 18 = 54°
y = 54°
∴ x + y = 180°
x + 54° = 180°
x = 180° - 54°
x = 126°
Thus, x = 126°
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