An illustration shows three rays extending from a common origin. The angle measures between them are labeled (x + 4) and (3x + 2). What are the two unknown angle measures that form the 90° angle?
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We are given two angle measures: (x + 4) and (3x + 2). We need to find the two unknown angle measures that form a 90° angle.
In a triangle, the sum of the three angles is always 180°. So, we can set up the equation:
(x + 4) + (3x + 2) + unknown angle measure = 180°.
Combining like terms, we have 4x + 6 + unknown angle measure = 180°.
Simplifying further, 4x + unknown angle measure = 174°.
To form a 90° angle, the two complementary angles must add up to 90°.
So, (x + 4) + (3x + 2) = 90.
Combining like terms, we have 4x + 6 = 90.
Subtracting 6 from both sides, we get 4x = 84.
Dividing both sides by 4, we find x = 21.
Now, we can substitute this value back into the equation to find the two angle measures:
(x + 4) = 21 + 4 = 25°
(3x + 2) = 3(21) + 2 = 65°
Therefore, the two unknown angle measures that form a 90° angle are 25° and 65°.
its wrong
The two unknown angle measures that form the 90° angle are labeled as ((x + 4)° ) and ( (3x + 2)° ). Since they form a right angle, their sum is 90°. We can set up an equation to find the value of ( x ):
(x + 4)° + (3x + 2)° = 90°
Solving this equation:
4x + 6 = 90
4x = 84
x = 21
So, the two angles are:
(21 + 4)° = 25° and (3(21) + 2)° = 65°
Therefore, the two unknown angle measures that form the 90° angle are 25° and 65°.
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To find the two unknown angle measures that form the 90° angle, we can set up an equation.
The sum of the three angles in a triangle is always 180°.
So, (x + 4) + (3x + 2) + unknown angle measure = 180°.
Combining like terms, we get 4x + 6 + unknown angle measure = 180°.
Simplifying further, we have 4x + unknown angle measure = 174°.
To form a 90° angle, two angles must add up to 90°.
So, one solution to the equation is when the unknown angle measure is 90°.
To find the second solution, we can subtract 90° from 174°:
174° - 90° = 84°.
Therefore, the two unknown angle measures that form the 90° angle are 90° and 84°.