Question

Triangle ESP is congruent to triangle DIR. In triangle ESP, the measurement of angle E is 40 degrees. In triangle DIR, angle I measures 60 degrees, and angle R is represented by the expression 2x + 32 degrees. Determine the value of 'x' that makes the triangles congruent, and then calculate the measurement of angle R in triangle DIR. Provide the solution for 'x' and the measurement of angle R.

Answer 1

To determine the value of 'x' that makes the triangles congruent, set up an equation and solve for x. The value of 'x' is 4. To calculate the measurement of angle R in triangle DIR, substitute the value of x into the expression 2x + 32. Angle R measures 40 degrees.

Step-by-step explanation:

To determine the value of 'x' that makes the triangles congruent, we need to find the measurement of angle R in triangle DIR. Since triangle ESP is congruent to triangle DIR, angle E is congruent to angle I, so angle I measures 40 degrees. We are given that angle I measures 60 degrees and angle R is represented by the expression 2x + 32 degrees. Setting up the equation, we have 2x + 32 = 40. Solving for x, we subtract 32 from both sides to get 2x = 8. Then we divide both sides by 2 to get x = 4. Therefore, the value of 'x' that makes the triangles congruent is 4.

To calculate the measurement of angle R, we substitute the value of x into the expression 2x + 32. Plugging in x = 4, we have 2(4) + 32 = 8 + 32 = 40. Therefore, the measurement of angle R in triangle DIR is 40 degrees.