Question
The triangles below are similar. In each triangle there is a 53 degrees angle and a right angle. What is the measure of the third angle in each triangle?
Triangle J K L. Angle K is 90 degrees and angle L is 53 degrees. Triangle Y X Z. Angle Y is 53 degrees and angle X is 90 degrees.
37º
47º
53º
127º
Triangle J K L. Angle K is 90 degrees and angle L is 53 degrees. Triangle Y X Z. Angle Y is 53 degrees and angle X is 90 degrees.
37º
47º
53º
127º
Answers
GPT-4o mini
In any triangle, the sum of the angles is always 180 degrees. Given that both triangles have a right angle (90 degrees) and another angle of 53 degrees, we can find the measure of the third angle by using the formula:
\[
\text{Third angle} = 180^\circ - (\text{Angle 1} + \text{Angle 2})
\]
For Triangle JKL:
- Angle K = 90 degrees
- Angle L = 53 degrees
Calculating the third angle (angle J):
\[
\text{Angle J} = 180^\circ - (90^\circ + 53^\circ) = 180^\circ - 143^\circ = 37^\circ
\]
For Triangle YXZ:
- Angle Y = 53 degrees
- Angle X = 90 degrees
Calculating the third angle (angle Z):
\[
\text{Angle Z} = 180^\circ - (90^\circ + 53^\circ) = 180^\circ - 143^\circ = 37^\circ
\]
In both triangles, the measure of the third angle is \( \mathbf{37^\circ} \).
\[
\text{Third angle} = 180^\circ - (\text{Angle 1} + \text{Angle 2})
\]
For Triangle JKL:
- Angle K = 90 degrees
- Angle L = 53 degrees
Calculating the third angle (angle J):
\[
\text{Angle J} = 180^\circ - (90^\circ + 53^\circ) = 180^\circ - 143^\circ = 37^\circ
\]
For Triangle YXZ:
- Angle Y = 53 degrees
- Angle X = 90 degrees
Calculating the third angle (angle Z):
\[
\text{Angle Z} = 180^\circ - (90^\circ + 53^\circ) = 180^\circ - 143^\circ = 37^\circ
\]
In both triangles, the measure of the third angle is \( \mathbf{37^\circ} \).