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.
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Here are the solutions for the marked angles: 1. Problem 1: The triangle is a right-angled triangle, so one angle is 90^. The sum of angles in a triangle is 180^. Step 1: Set up the equation for the sum of angles. x + 90^ + 40^ = 180^ Step 2: Combine the known angles. x + 130^ = 180^ Step 3: Solve for x. x = 180^ - 130^ x = 50^ The value of x is 50^. 2. Problem 2: The markings indicate that it is an isosceles triangle, meaning the two base angles are equal. One base angle is 50^, so the other base angle is also 50^. The sum of angles in a triangle is 180^. Step 1: Set up the equation for the sum of angles. y + 50^ + 50^ = 180^ Step 2: Combine the known angles. y + 100^ = 180^ Step 3: Solve for y. y = 180^ - 100^ y = 80^ The value of y is 80^. 3. Problem 3: The markings indicate that all three sides of the triangle are equal, making it an equilateral triangle. All angles in an equilateral triangle are equal. The sum of angles in a triangle is 180^. Step 1: Divide the total angle sum by 3. k = (180^)/(3) Step 2: Calculate the value of k. k = 60^ The value of k is 60^. 4. Problem 4: The markings indicate that two sides of the triangle are equal, making it an isosceles triangle. The angles opposite the equal sides are equal. Step 1: Set the angles opposite the equal sides equal to each other. 2a = 62^ Step 2: Solve for a. a = (62^)/(2) a = 31^ The value of a is 31^. 5. Problem 5: The markings indicate that sides AB and AC are equal, making it an isosceles triangle. The exterior angle at B is 108^. Step 1: Find the interior angle at B. Angles on a straight line sum to 180^. ABC = 180^ - 108^ = 72^ Step 2: Since AB = AC, the base angles opposite these sides are equal. ACB = ABC = 72^ Step 3: The sum of angles in triangle ABC is 180^. Set up the equation for the sum of angles. y + 72^ + 72^ = 180^ Step 4: Combine the known angles and solve for y. y + 144^ = 180^ y = 180^ - 144^ y = 36^ The value of y is 36^. 6. Problem 6: The triangle is a right-angled triangle, so one angle is 90^. The sum of angles in a triangle is 180^. Step 1: Set up the equation for the sum of angles. 90^ + 65^ + marked angle = 180^ Step 2: Combine the known angles. 155^ + marked angle = 180^ Step 3: Solve for the marked angle. marked angle = 180^ - 155^ marked angle = 25^ The value of the marked angle is 25^. Send me the next one 📸