Question

" Find the value of (x). Then find the measure of each angle given (m_1 = (x+30)^°), (m_2 = (5x-25)^°), and (m_3 = (4x)^°).

a) (x = 10^°), (m_1 = 40^°), (m_2 = 25^°), (m_3 = 40^°)
b) (x = 20^°), (m_1 = 50^°), (m_2 = 75^°), (m_3 = 80^°)
c) (x = 15^°), (m_1 = 45^°), (m_2 = 50^°), (m_3 = 60^°)
d) (x = 30^°), (m_1 = 60^°), (m_2 = 95^°), (m_3 = 120^°)
"

Answer 1

Upon examining option (d), the calculated angles based on the given expressions for angles do not match the proposed answers. Calculations show that if x = 30°, m_1 = 60°, m_2 = 125°, and m_3 = 120°, contrary to the values provided.

Step-by-step explanation:

The question asks us to determine the value of x and calculate the measure of each angle based on given expressions for m_1, m_2, and m_3. Without additional context or information, such as the relationship between the angles (are they complementary, supplementary, or part of a geometric figure?), we cannot definitively solve for the value of x. However, we can check the proposed answers to see if they are consistent with the given expressions for each angle.

Let's examine option (d):

1. If x = 30°, then m_1 = (x + 30)° = (30° + 30°) = 60°.
2. The measure of angle m_2 using the expression m_2 = (5x - 25)° would be m_2 = (5 × 30° - 25°) = 125°, not 95° as stated.
3. Lastly, angle m_3 would be calculated using m_3 = (4x)°, resulting in m_3 = (4 × 30°) = 120°.

From this, we can see that the values provided in option (d) are incorrect because the calculations for m_2 do not match the stated 95°.