Question

Find the value of x by filling the blanks in the provided statement-reason solutions. a Statement Reason

a. m∠A +m∠B +m∠C=
b. 28°+x−4° + ______ = 180°
c. x=_______

Answer 1

To find the value of x in a triangle where the sum of angles equals 180 degrees, add the given angles, subtract from 180, and solve for x. In this case, x is found to be 148 degrees.

Step-by-step explanation:

To find the value of x, we use the fact that the sum of the angles in a triangle is 180 degrees. Given m∠A + m∠B + m∠C = 180° and one of the angles is expressed as x - 4°, the statement and reason for the solution are:

• a. m∠A + m∠B + m∠C = 180° (The sum of the angles in a triangle is 180°).
• b. 28° + x - 4° + m∠C = 180° (Substitute given angle measures).
• c. To find x, you need to add 28° to 4°, subtract that from 180°, and then isolate x.

By doing the calculations:

• 28° + 4° = 32°
• 180° - 32° = 148°
• So, x = 148°

Thus, the missing values for the provided statement-reason solutions are:

• b. m∠C = 148°
• c. x = 148°