△GHI∼△LKJ , and m∠G=30° , m∠H=80° , and m∠I=70° . What are the measures of angles J , K , and L ? (2 points)
m∠J =
°, m∠K =
°, and m∠L =
°
To find the measures of angles J, K, and L, we need to apply the angle sum property for triangles.
In triangle GHI, the sum of the interior angles is 180°:
m∠G + m∠H + m∠I = 180°
30° + 80° + 70° = 180°
Therefore, m∠J (angle J) is 180° - (m∠G + m∠H + m∠I):
m∠J = 180° - (30° + 80° + 70°)
m∠J = 180° - 180°
m∠J = 0°
Next, we look at triangle LKJ. Since J and K are vertical angles (opposite angles), they have the same measure. Therefore:
m∠J = m∠K
m∠K = 0°
Finally, to find m∠L, we apply the angle sum property in triangle LKJ:
m∠L + m∠K + m∠J = 180°
m∠L + 0° + 0° = 180°
m∠L = 180° - 0°
m∠L = 180°
So, the measures of angles J, K, and L are:
m∠J = 0°
m∠K = 0°
m∠L = 180°
wrong
Apologies for the mistake. Let's solve it correctly.
Given: ∆GHI is similar to ∆LKJ.
m∠G = 30°, m∠H = 80°, m∠I = 70°.
In similar triangles, corresponding angles are equal.
Since ∆GHI is similar to ∆LKJ, we can say:
m∠H = m∠K
m∠I = m∠J
Using the given values:
m∠H = m∠K
80° = m∠K
m∠I = m∠J
70° = m∠J
Now, to find m∠L, we use the angle sum property for triangle LKJ:
m∠K + m∠J + m∠L = 180°
Substituting the values we found earlier:
80° + 70° + m∠L = 180°
150° + m∠L = 180°
To isolate m∠L, we subtract 150° from both sides:
m∠L = 180° - 150°
m∠L = 30°
Therefore, the measures of angles J, K, and L are:
m∠J = 70°
m∠K = 80°
m∠L = 30°