Maharashtra Board Class 7 Chapter 4 Set 16 Angles and Pairs of Angles Solutions

Question 1. The measures of some angles are given below. Write the measures of their complementary angles.
(i) 40°
(ii) 63°
(iii) 45°
(iv) 55°
(v) 20°
(vi) 90°
(vii) x°
Answer:
Solution:
(i) Let the measure of the complementary angle be x°.
.. \(40 + x = 90\)
.. \(40 + x - 40 = 90 - 40\)
....(Subtracting 40 from both sides)
.. \(x = 50\)
.. The measure of the complement of an angle of measure 40° is 50°.
(ii) Let the measure of the complementary angle be x°.
.. \(63 + x = 90\)
.. \(63+x-63 = 90-63\)
....(Subtracting 63 from both sides)
.. \(x = 27\)
.. The measure of the complement of an angle of measure 63° is 27°.
(iii) Let the measure of the complementary angle be x°.
.. \(45 + x = 90\)
.. \(45+x-45 = 90-45\)
....(Subtracting 45 from both sides)
.. \(x = 45\)
.. The measure of the complement of an angle of measure 45° is 45°.
(iv) Let the measure of the complementary angle be x°.
.. \(55 + x = 90\)
.. \(55 + x-55 = 90-55\)
....(Subtracting 55 from both sides)
.. \(x = 35\)
.. The measure of the complement of an angle of measure 55° is 35°.
(v) Let the measure of the complementary angle be x°.
.. \(20 + x = 90\)
.. \(20 + x - 20 = 90 - 20\)
....(Subtracting 20 from both sides)
.. \(x = 70\)
.. The measure of the complement of an angle of measure 20° is 70°.
(vi) Let the measure of the complementary angle be x°.
.. \(90 + x = 90\)
.. \(90 + x - 90 = 90 - 90\)
....(Subtracting 90 from both sides)
.. \(x = 0\)
.. The measure of the complement of an angle of measure 90° is 0°.
(vii) Let the measure of the complementary angle be a°.
.: \(x + a = 90\)
∴ \(x + a - x = 90 - x\)
....(Subtracting x from both sides)
.. \(a = (90 - x)\)
.. The measure of the complement of an angle of measure x° is (90 - x)°.
In simple words: Complementary angles sum up to 90 degrees. To find the complementary angle of a given angle, subtract the given angle from 90 degrees. For an angle x°, its complement is (90 - x)°.

🎯 Exam Tip: Remember the definition of complementary angles (sum to 90°) to quickly solve problems involving finding the complement of an angle. Be careful with algebraic expressions.

Question 2. (y – 20)° and (y + 30)° are the measures of complementary angles. Find the measure of each angle.
Answer:
Solution:
(y – 20)° and (y + 30)° are the measures of complementary angles.
.. \((y - 20) + (y + 30) = 90\)
∴ \(y + y + 30 - 20 = 90\)
.. \(2y+10 = 90\)
.. \(2y = 90 - 10\)
.. \(2y = 80\)
.. \(y = \frac{80}{2}\)
\( = 40\)
Measure of first angle = \((y - 20)° = (40 - 20)° = 20°\)
Measure of second angle = \((y + 30)° = (40 + 30)° = 70°\)
.. The measure of the two angles is 20° and 70°.
In simple words: Since the two given angles are complementary, their sum must be 90 degrees. Set up an equation with their sum equal to 90, solve for 'y', and then substitute 'y' back into the angle expressions to find their individual measures.

🎯 Exam Tip: When dealing with algebraic expressions for angles, ensure you solve for the variable first, then substitute its value back into *all* angle expressions to find the final measures. Show each step clearly.

Maharashtra Board Class 7 Maths Chapter 4 Angles And Pairs Of Angles Practice Set 16 Intext Questions And Activities

Question 1. Observe the angles in the figure and enter the proper number in the empty place.

ℹ️ चित्र व्याख्या (Diagram Explanation): इस चित्र में दो कोण दर्शाए गए हैं। पहला कोण ABC है जिसका माप 40° है। दूसरा कोण PQR है जिसका माप 50° है। दोनों कोणों को अलग-अलग दिखाया गया है, और उनके शीर्ष तथा भुजाएँ स्पष्ट रूप से अंकित हैं।
Answer:
Solution:
1. \(m\angle ABC = 40\)°
2. \(m\angle PQR = 50\)°
3. \(m\angle ABC + m\angle PQR = 90\).
In simple words: The diagram shows two angles, ∠ABC and ∠PQR, measuring 40° and 50° respectively. When these two angle measures are added together, their sum is 90°, which means they are complementary angles.

🎯 Exam Tip: Accurately reading angle measures from diagrams and understanding the definition of complementary angles (sum is 90°) are key to solving such problems. Always check if the sum indeed equals 90° for complementary pairs.