The tip of the triangle is (8x + 5)° the left side of the triangle is (5x - 1)° and the bottom of the triangle is (4x + 6)°
Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.
• 46°, 50°, and 85°
• 42°, 44°, and 79°
• 46°, 49°, and 85°
• 50°, 54°, and 93°
To find the measures of each angle for the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.
Let's set up an equation using the information given:
(8x + 5) + (5x - 1) + (4x + 6) = 180
Combine like terms:
17x + 10 = 180
Subtract 10 from both sides:
17x = 170
Divide by 17:
x = 10
Now, substitute x = 10 into the expressions for each angle measure:
Top angle measure: 8x + 5 = 8(10) + 5 = 85
Left side angle measure: 5x - 1 = 5(10) - 1 = 49
Bottom angle measure: 4x + 6 = 4(10) + 6 = 46
Therefore, the measures of each angle for the triangle are 46°, 49°, and 85°. Therefore, the correct answer is:
• 46°, 49°, and 85°