CBSE Class 7 Mathematics Lines and Angles Assignment Set 03

FA II HOME WORK 2 (LINES AND ANGLES) CLASS VII

Q1 Among two supplementary angles, the measure of the larger angle is \(36^\circ\) more than the measure of the smaller. Find the measure of each angle?
Answer: Let the measure of the smaller angle be \(x^\circ\).
Then the measure of the larger angle is \((x + 36)^\circ\).
Since the two angles are supplementary, their sum is \(180^\circ\).
\(x + (x + 36) = 180\)
\(2x + 36 = 180\)
\(2x = 180 - 36\)
\(2x = 144\)
\(x = \frac{144}{2} = 72\)
Smaller angle = \(72^\circ\)
Larger angle = \(72 + 36 = 108^\circ\)
In simple words: Supplementary angles add up to \(180^\circ\), so we set up an equation with the smaller angle as \(x\) and solved for it.

Exam Tip: Always remember that supplementary angles sum up to \(180^\circ\) and complementary angles sum up to \(90^\circ\).

Q2 Using the given figure, find the measure of \(\angle AOC\) and \(\angle BOC\)
Answer: From the given figure, \(\angle AOC\) and \(\angle BOC\) form a linear pair on the straight line \(AB\).
Therefore, the sum of their measures is \(180^\circ\).
\(\angle AOC + \angle BOC = 180^\circ\)
\((2x - 10)^\circ + (3x + 20)^\circ = 180^\circ\)
\(2x - 10 + 3x + 20 = 180\)
\(5x + 10 = 180\)
\(5x = 180 - 10\)
\(5x = 170\)
\(x = \frac{170}{5} = 34\)
Now, substitute the value of \(x\):
\(\angle AOC = 2(34) - 10 = 68 - 10 = 58^\circ\)
\(\angle BOC = 3(34) + 20 = 102 + 20 = 122^\circ\)
In simple words: Angles on a straight line add up to \(180^\circ\), so we equated their sum to \(180\) to find \(x\) and then substituted it back.

Exam Tip: Verify your answer by adding the calculated angles: \(58^\circ + 122^\circ = 180^\circ\).

Q3 Using the given figure, find the measure of \(x\)
Answer: From the given figure, the angles on the straight line \(AB\) at point \(O\) form a straight angle, which measures \(180^\circ\).
\(65^\circ + x^\circ + 70^\circ = 180^\circ\)
\(135 + x = 180\)
\(x = 180 - 135\)
\(x = 45\)
In simple words: The sum of all adjacent angles on a straight line is always \(180^\circ\).

Exam Tip: Combine all known numerical values on the straight line before subtracting from \(180^\circ\).

Q4 Using the given figure, find the value of \(x\) and \(y\)
Answer: From the given figure, line \(RS\) and line \(PQ\) intersect at point \(O\).
Vertical angles are equal.
\(y^\circ = 42^\circ \implies y = 42\)
Also, \(\angle POR\) and \(\angle x\) form a linear pair on the straight line \(RS\).
\(42^\circ + x^\circ = 180^\circ\)
\(x = 180 - 42\)
\(x = 138\)
In simple words: Vertically opposite angles are equal, and angles forming a linear pair add up to \(180^\circ\).

Exam Tip: Look for intersecting lines to identify vertically opposite angles directly.

Q5 Find the value of \(x\) in the given figure
Answer: The sum of all angles around a complete point is \(360^\circ\).
\(100^\circ + x^\circ + 46^\circ + 74^\circ = 360^\circ\)
\(100 + 46 + 74 + x = 360\)
\(220 + x = 360\)
\(x = 360 - 220\)
\(x = 140\)
In simple words: A full circle around a point measures \(360^\circ\), so the sum of all surrounding angles equals \(360^\circ\).

Exam Tip: When multiple angles surround a single point, always use the complete angle sum property of \(360^\circ\).