To find angle \( b \) in the right triangle, we can use the property of exterior angles. The exterior angle is equal to the sum of the two opposite interior angles.
Given that the exterior angle is 142 degrees, we can set up the equation:
\[ \text{Exterior angle} = a + b \]
So, we have:
\[ 142 = a + b \]
Since this is a right triangle, we know that \( a + b = 90 \) degrees (because the right angle is 90 degrees).
Now we have two equations:
- \( a + b = 90 \)
- \( a + b = 142 \)
Using the first equation to isolate \( a \):
\[ a = 90 - b \]
Substituting this into the second equation:
\[ 142 = (90 - b) + b \]
This simplifies to:
\[ 142 = 90 \]
This is not possible, which means we need to reevaluate how we can relate the angles.
We can express the relationship more clearly: the exterior angle (142 degrees) is equal to 90 degrees (the right angle) plus angle \( a \):
\[ 142 = 90 + a \]
From this, we can solve for angle \( a \):
\[ a = 142 - 90 = 52 \]
Now that we have \( a \), we can find angle \( b \):
Using the first equation again:
\[ a + b = 90 \]
Substituting \( a = 52 \):
\[ 52 + b = 90 \]
Now, solving for \( b \):
\[ b = 90 - 52 = 38 \]
Thus, angle \( b \) is \( 38° \).
The answer is 38°.
3 answers