/_1 and /_2 are vertical angles. If m/_1=(x+2)^(@) and m/_2=(3x-8)^(@), then find the measure of /_1. Answer:

Question

/_1 and  /_2 are vertical angles. If  m/_1=(x+2)^(@) and  m/_2=(3x-8)^(@), then find the measure of  /_1. Answer:

Bytelearn · Accepted Answer

Set Angle Expressions Equal: Vertical angles are congruent, so their measures are equal. Set the expressions for the measures of angle 1 and angle 2 equal to each other to find the value of x. (x + 2)^2 = (3x - 8)^2Expand and Solve Equation: Expand both sides of the equation to solve for x. (x + 2)(x + 2) = (3x - 8)(3x - 8) x^2 + 4x + 4 = 9x^2 - 48x + 64Rearrange and Set to Zero: Rearrange the equation to bring all terms to one side and set the equation to zero. x^2 - 9x^2 + 4x + 48x + 4 - 64 = 0 -8x^2 + 52x - 60 = 0Simplify and Divide: Divide the entire equation by -4 to simplify. (-8x^2 + 52x - 60) / -4 = 0 / -4 2x^2 - 13x + 15 = 0Factor Quadratic Equation: Factor the quadratic equation to find the values of x. (2x - 3)(x - 5) = 0Solve for x: Set each factor equal to zero and solve for x. 2x - 3 = 0 or x - 5 = 0 x = 3/2 or x = 5Check Validity of x: Since x represents a measure of an angle, it should be a positive value. Both 3/2 and 5 are positive, so we need to check which one is valid by substituting back into the original expressions for the angle measures. Substitute x = 3/2 into (x + 2)^2: (3/2 + 2)^2 = (5/2)^2 = (2.5)^2 = 6.25 Substitute x = 3/2 into (3x - 8)^2: (3(3/2) - 8)^2 = (4.5 - 8)^2 = (-3.5)^2 = 12.25 Since these are not equal, x = 3/2 is not the correct value.Substitute x = 5: Now, substitute x = 5 into (x + 2)^2: (5 + 2)^2 = 7^2 = 49 Substitute x = 5 into (3x - 8)^2: (3(5) - 8)^2 = (15 - 8)^2 = 7^2 = 49 Since these are equal, x = 5 is the correct value.Find Measure of Angle 1: Now that we have the correct value of x, we can find the measure of angle 1. m/_1 = (x + 2)^2 m/_1 = (5 + 2)^2 m/_1 = 7^2 m/_1 = 49 degrees

$\angle 1$ and $\angle 2$ are vertical angles. If $\mathrm{m} \angle 1=(x+2)^{\circ}$ and $\mathrm{m} \angle 2=(3 x-8)^{\circ}$ , then find the measure of $\angle 1$ . $\newline$ Answer:

Full solution

More problems from Transformations of quadratic functions

Related topics

∠1 \angle 1 ∠1 and ∠2 \angle 2 ∠2 are vertical angles. If m∠1=(x+2)∘ \mathrm{m} \angle 1=(x+2)^{\circ} m∠1=(x+2)∘ and m∠2=(3x−8)∘ \mathrm{m} \angle 2=(3 x-8)^{\circ} m∠2=(3x−8)∘, then find the measure of ∠1 \angle 1 ∠1.\newlineAnswer:

$\angle 1$ and $\angle 2$ are vertical angles. If $\mathrm{m} \angle 1=(x+2)^{\circ}$ and $\mathrm{m} \angle 2=(3 x-8)^{\circ}$ , then find the measure of $\angle 1$ . $\newline$ Answer: