Questions: Example 2: Find x and the measures of all of the angles

Example 2: Find x and the measures of all of the angles
Transcript text: Example 2: Find $x$ and the measures of all of the angles
failed

Solution

failed
failed

Solution Steps

Step 1: Set up the equation

The given angles are supplementary, meaning their sum is 180 degrees. Therefore, we can set up the equation: \[ (2x + 9) + 115 = 180 \]

Step 2: Simplify the equation

Combine like terms: \[ 2x + 124 = 180 \]

Step 3: Solve for x

Subtract 124 from both sides: \[ 2x = 56 \] Divide by 2: \[ x = 28 \]

Step 4: Find the measure of angle 1

Substitute \( x = 28 \) back into the expression for the angle: \[ 2x + 9 = 2(28) + 9 = 56 + 9 = 65 \]

Step 5: Find the measure of angle 2

Since angle 2 is given as 115 degrees, we already know its measure.

Final Answer

  • \( x = 28 \)
  • \( \angle 1 = 65^\circ \)
  • \( \angle 2 = 115^\circ \)
Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Let p and q represent the following simple statements. p : I get a raise. q: I work hard. Write the following compound statement in symbolic form. I get a raise if and only if I work hard. The compound statement written in symbolic form is p if and only if q.
failedAnswered
f(x) is defined as follows: - For 0 < x < 3, f(x) = -(x-3)^2 + 8 - For x = 3, f(x) = 3 - For 3 < x < 6, f(x) = -x + 7 Find f(1).
failedAnswered
The text details how Five Guys identified that their target market values taste, freshness, and quality and are willing to pay a premium price for a "gourmet" hamburger experience. How did market segmentation help Five Guys in this example? - It helped Five Guys plan a repositioning statement. - It helped Five Guys design new menu items - It helped Five Guys in targeting lower income families. - It helped Five Guys define the needs and wants of their customer. - It helped Five Guys organize a database.
failedAnswered
2. If you never receive immediate feedback from your audience big or small but you prepare as though you do by anticipating their responses and presenting a spoken message to the masses; what should you think?
failedAnswered
The volume of a cone with height h and radius r can be found using the formula V=1/3 π r^2 h Find the volume of a cone with radius 7 feet and height 4 feet. ft^3