Question 2 - Figure it out - Page 165 - Sum of angles of a triangle - Chapter 7 Class 7 - A tale of three Intersecting Lines (Ganit Prakash)

Transcript

Question 2 - Figure it out - Page 165 Can you construct a triangle all of whose angles are equal to 70°? If two of the angles are 70° what would the third angle be? If all the angles in a triangle have to be equal, then what must its measure be? Explore and find out. Let’s answer this one by one Can you construct a triangle all of whose angles are equal to 70°? Our figure would look like Since XY is a line Applying Linear Pair ∠ XAB + ∠ A + ∠ YAC = 180° 70° + 70° + 70° = 180° 210° = 180° But this is not true So, this triangle is not possible If two of the angles are 70° what would the third angle be? Our figure would look like Since XY is a line Applying Linear Pair ∠ XAB + ∠ A + ∠ YAC = 180° 70° + ∠ A + 70° = 180° ∠ A + 140° = 180° ∠ A = 180° – 140° ∠ A = 40° So, the third angle would be 40° If all the angles in a triangle have to be equal, then what must its measure be? Let’s draw our figure Let all angles be x Now, by alternate interior angles ∠XAB = x° ∠YAC = x° Since XY is a line Applying Linear Pair ∠ XAB + ∠ A + ∠ YAC = 180° x° + x° + x° = 180° 3x° = 180° x = (180° )/3 x = 60° Thus, if all angles of triangle are equal, then each angle would be 60°