In the given figure, the three parallel lines are cut through by a transversal. Of the marked angles, the greater two are of equal measure. The ratio of a greater angle to the smaller angle is 7 : 3. What is the measure of the greater angle?
To solve this problem, let's analyze the given figure and the conditions:
The figure consists of three parallel lines AB, CD, and EF, which are intersected by a transversal line. Let's denote the angles as follows:
- Angle X on line AB
- Angle Y on line CD
- Angle Z on line EF
Given that:
- The greater two angles are equal.
- The ratio of a greater angle to the smaller angle is 7:3.
Since the greater two angles are equal, let us assume these angles are X and Z. Therefore, X = Z.
According to the properties of parallel lines intersected by a transversal, angle Y is the smaller angle. We express this relationship as:
\(\frac{X}{Y} = \frac{7}{3}\)
Let the measure of the smaller angle Y be \(3x\). Then, the measure of the greater angle X (or Z) is \(7x\).
Since angle X, angle Y, and angle Z form a straight line when added together, we have:
\(X + Y + Z = 180^\circ\)
Substituting the values, we get:
\(7x + 3x = 180^\circ\)
\(10x = 180^\circ\)
\(x = 18^\circ\)
Thus, the measure of the greater angle X (or Z) is:
\(7x = 126^\circ\)
Hence, the measure of the greater angle is 126°. Therefore, the correct answer is:
126°
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What is the sum of the angle complementary to $15^\circ$ and the angle supplementary to $125^\circ$?
Important Questions from Lines and Angles
If angles of a triangle are in the ration of 2 : 3 : 4, then the measure of the smallest angle is:
In the triangle, if AB = AC and ∠ABC = 72°, then ∠BAC is:
The angles of a triangle are (8x - 15)°,(6x - 11)° and ( 4x – 10)°. What is the value of x ?
In a ΔABC, the bisectors of ∠B and ∠C meet at point O, inside the triangle. If ∠BOC = 122°, then the measure of ∠A is:
In ΔABC, D is a point on side BC such that ∠ADC = 2∠BAD. If ∠A = 80° and ∠C = 38°, then what is the measure of ∠ADB?
