This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions for the remaining problems in the image: a) Step 1: Identify the interior angles of the triangle. The triangle has two interior angles given as 70^ and 70^. The third interior angle can be found using the angle sum property of a triangle. Third interior angle = 180^ - 70^ - 70^ = 180^ - 140^ = 40^. Step 2: Determine the exterior angle a. The exterior angle a is adjacent to one of the 70^ interior angles, forming a linear pair. a = 180^ - 70^ a = 110^ Alternatively, the exterior angle is equal to the sum of the two opposite interior angles: a = 70^ + 40^ a = 110^ The value of a is 110^. b) Step 1: Identify the interior angles of the triangle. The triangle has two interior angles given as 60^ and 60^. The third interior angle can be found using the angle sum property of a triangle. Third interior angle = 180^ - 60^ - 60^ = 180^ - 120^ = 60^. This means it is an equilateral triangle. Step 2: Determine the exterior angle b. The exterior angle b is adjacent to one of the 60^ interior angles, forming a linear pair. b = 180^ - 60^ b = 120^ Alternatively, the exterior angle is equal to the sum of the two opposite interior angles: b = 60^ + 60^ b = 120^ The value of b is 120^. c) Step 1: Identify the relationship between the interior angle C and the given exterior angle. The exterior angle given is 105^, and it forms a linear pair with the interior angle C. C + 105^ = 180^ Step 2: Solve for C. C = 180^ - 105^ C = 75^ We can verify this using the angle sum property of the triangle. The other two interior angles are 30^ and 75^. 30^ + 75^ + C = 180^ 105^ + 75^ = 180^ 180^ = 180^ This confirms the value of C. The value of C is 75^. Last free one today — make it count tomorrow, or type /upgrade for unlimited.