GSEB Class 7 Maths Solutions Chapter 6 ત્રિકોણ અને તેના ગુણધર્મો Exercise 6.2

Gujarat Board Textbook Solutions Class 7 Maths Chapter 6 ત્રિકોણ અને તેના ગુણધર્મો Ex 6.2

Question 1. નીચેની આકૃતિઓમાં બહિષ્કોણનું માપ શોધો
Answer: For each diagram shown above, the exterior angle of a triangle is equal to the sum of the two interior opposite angles. In every figure provided, the exterior angle is marked as \( x \). We need to find the value of this angle.
(i) \( \angle x = 50^\circ + 70^\circ = 120^\circ \)
(ii) \( \angle x = 65^\circ + 45^\circ = 110^\circ \)
(iii) \( \angle x = 30^\circ + 40^\circ = 70^\circ \)
(iv) \( \angle x = 60^\circ + 60^\circ = 120^\circ \)
(v) \( \angle x = 50^\circ + 50^\circ = 100^\circ \)
(vi) \( \angle x = 30^\circ + 60^\circ = 90^\circ \)
In simple words: To find the exterior angle of a triangle, just add the two opposite inside angles together. This rule applies to all the shapes shown here.

Exam Tip: Remember that the exterior angle of a triangle is always equal to the sum of its two opposite interior angles. This is a fundamental property to remember.

Question 2. નીચેની આકૃતિઓમાં અંદરના અજ્ઞાત ખૂણાનું માપ શોધોઃ
Answer: For each figure given, the measure of a triangle's exterior angle equals the sum of its known interior opposite angle and the unknown interior opposite angle. Therefore, the measure of the unknown interior opposite angle \( x \) can be found by subtracting the measure of the known interior opposite angle from the exterior angle of the triangle.
(i) અજ્ઞાત અંતસંમુખકોણ \( x \)નું માપ \( = 115^\circ – 50^\circ = 65^\circ \)
(ii) અજ્ઞાત અંતઃસંમુખકોણ \( x \)નું માપ \( = 100^\circ – 70^\circ = 30^\circ \)
(iii) અજ્ઞાત અંતઃસંમુખકોણ \( x \)નું માપ \( = 125^\circ – 90^\circ = 35^\circ \)
(iv) અજ્ઞાત અંતઃસંમુખકોણ \( x \)નું માપ \( = 120^\circ – 60^\circ = 60^\circ \)
(v) અજ્ઞાત અંતઃસંમુખકોણ \( x \)નું માપ \( = 80^\circ – 30^\circ = 50^\circ \)
(vi) અજ્ઞાત અંતઃસંમુખકોણ \( x \)નું માપ \( = 75^\circ – 35^\circ = 40^\circ \)
In simple words: When you know the outside angle and one inside opposite angle, you can get the other inside opposite angle by taking away the known inside angle from the outside angle.

Exam Tip: Always recall the exterior angle theorem, which states that the exterior angle equals the sum of the two opposite interior angles. Use this to either find the exterior angle or an unknown interior angle.