Question

In ΔRST, \text{m}\angle R = (5x-11)^{\circ}m∠R=(5x−11)

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, \text{m}\angle S = (3x-3)^{\circ}m∠S=(3x−3)
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, and \text{m}\angle T = (3x+18)^{\circ}m∠T=(3x+18)
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. Find \text{m}\angle R.m∠R.

Answer 1

To determine the measure of angle R, we use the sum of angles in a triangle, which is 180 degrees. By setting up an equation with the given expressions for the angles and solving for x, we find angle R measures 69 degrees.

Step-by-step explanation:

To find the measure of angle R in triangle RST, we can use the fact that the sum of the angles in any triangle is 180 degrees. We are given:

• m R = (5x-11)°
• m S = (3x-3)°
• m T = (3x+18)°

Combining these equations, we get:

(5x - 11)° + (3x - 3)° + (3x + 18)° = 180°

Adding the equations gives:

11x + 4 = 180

Solving for x, we get:

x = 16

Substituting x back into the expression for m R:

m R = (5(16) - 11)° = 69°

Therefore, the measure of angle R is 69 degrees.