Question

Find the value of x in the given equations:

m∠DEV = 69x + 2,
m∠DEF = 79x + 3,
m∠VEF = 21°.

Answer 1

To find the value of x, we use the fact that the angles in a triangle sum up to 180 degrees. By adding the given equations representing the angles of triangle DEF and equating their sum to 180 degrees, we can solve for x, resulting in an approximate value of 1.04.

Step-by-step explanation:

To find the value of x in the given equations, we will use the fact that in a triangle, the sum of the angles equals 180 degrees. In this case, the triangle is formed by the angles DEV, DEF, and VEF. As stated, we have the equation m∠DEV = 69x + 2, the equation m∠DEF = 79x + 3, and we are given m∠VEF = 21°.

Summing these three angles should equal 180 degrees:

1. m∠DEV + m∠DEF + m∠VEF = 180°
2. (69x + 2) + (79x + 3) + 21 = 180
3. 69x + 79x + 26 = 180
4. 148x + 26 = 180
5. 148x = 180 - 26
6. 148x = 154
7. x = 154 / 148
8. x = 1.04

Therefore, the value of x is approximately 1.04.