Question
What is angle $x$ in the schematic diagram given below?
The correct answer is
30
Step 1: Convert exterior angles into interior angles
Each marked angle is an exterior angle of $130^\circ$.
So, corresponding interior angle:
$180^\circ - 130^\circ = 50^\circ$
Thus, the two relevant interior angles are $50^\circ$ each.
Step 2: Analyze the line inclinations
The upper slanted line makes an angle of $50^\circ$ with the middle line.
Similarly, the lower slanted line also forms a related $50^\circ$ angle, but on the opposite side.
Using the geometry of the intersecting lines, the acute angle between the two slanted segments becomes:
$ x = 50^\circ - 20^\circ $
Step 3: Calculate $x$
$ x = 30^\circ $
Final Answer:
$\boxed{30^\circ}$
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Important Questions from Geometry (Notes)
- Which of the following is not true for a parallelogram?
- A 6 cm long chord of a circle is at a distance of 4 cm from the centre of the circle. Find the distance of 8 cm long chord of the same circle from the centre.
- The length of major axis and coordinate of vertices for the ellipse $3x^2 + 2y^2 = 6$ respectively are:
- If the line through (3, y) and (2, 7) is parallel to the line through (-1, 4) and (0,6), then the value of y is:
- The points (K, 2 – 2K), (-K +1,2K) and (-4-K, 6-2K) are collinear if:
(A) K = $\frac{1}{2}$
(B) K = $-\frac{1}{2}$
(C) K = $\frac{3}{2}$
(D) K = -1
(E) K = 1
Choose the correct answer from the options given below:
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