Answer:
m∠QPT = 110°
Step-by-step explanation:
1. We can use exterior angle theorem to find m∠QPT. Exterior Angle Theorem states that the exterior angle of a triangle is equal to the sum of the two remote angles in that same triangle.
- This means that 6x + 20 = x + 40 + 4x - 5. Then, we can plug in the value of x into 6x + 20 and find the measure of ∠QPT.
2. (Solving)
Step 1: Combine like terms.
- [tex]6x + 20 = (x+4x)+(40-5)[/tex]
- [tex]6x + 20 = 5x + 35[/tex]
Step 2: Subtract 20 from both sides.
- [tex]6x + 20 - 20 = 5x + 35 - 20[/tex]
- [tex]6x = 5x +15[/tex]
Step 3: Subtract 5x from both sides.
- [tex]6x - 5x = 5x +15 - 5x[/tex]
- [tex]x = 15[/tex]
Step 4: Check if solution is correct.
- [tex]6(15)+20=(15)+40+4(15)-5[/tex]
- [tex]90 + 20 = 15 + 40 + 60 - 5[/tex]
- [tex]110 = 55 + 60 - 5[/tex]
- [tex]110 = 115 - 5[/tex]
- [tex]110 = 110[/tex]
3. Now, let's plug in 15 for 6x + 20:
- [tex]90+20[/tex]
- [tex]110[/tex]
Therefore, m∠QPT = 110°.
