A triangle has an angle that measures 105°. The other two angles are in a ratio of 7:8. What are the measures of those two angles?
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To find the measures of the other two angles, let's start by finding the total sum of the three angles in a triangle:
In any triangle, the sum of the three angles is always 180°.
Let's call one of the angles x. According to the given ratio, the other angle would be 7x and 8x.
So, we can set up the equation:
x + 7x + 8x = 180
Combining like terms, we have:
16x = 180
To solve for x, we divide both sides of the equation by 16:
x = 180 / 16
x = 11.25
Now we can find the values of the other two angles:
Angle 1 = 7x = 7 * 11.25 = 78.75°
Angle 2 = 8x = 8 * 11.25 = 90°
To find the measures of the other two angles in the triangle, we first need to know that the sum of all angles in a triangle is always 180°.
Let's represent the measures of the other two angles as 7x and 8x, where x is a common factor. The ratio given tells us that the first angle measures 7x and the second angle measures 8x.
We know that the sum of all three angles is 180°. So, we can set up an equation:
105° + 7x + 8x = 180°
Combining like terms:
105° + 15x = 180°
Now, we can solve for x by subtracting 105° from both sides:
15x = 180° - 105°
15x = 75°
Next, divide both sides by 15 to isolate x:
x = 75° / 15
x = 5°
Now that we have found the value of x, we can substitute it back into the original expressions for the two angles:
First angle = 7x = 7(5°) = 35°
Second angle = 8x = 8(5°) = 40°
Therefore, the measures of the other two angles are 35° and 40°.
105+7A+8A=180
solve for A
then the angles are 7A, and 8A