Answer:
y° = 25°
Explanation:
Given the diagram of a triangle, where it shows an exterior angle with a measure of ∠115°, and that an angle bisector bisects the triangle into two right triangles.
According to the Exterior Angle Theorem, the measure of the exterior angle is equal to the sum of the measures of two non-adjacent interior angles. In other words, the given exterior angle, m∠115° is equal to m∠y° + m∠90°.
Solve for y:
Hence, we could simply solve for the value of y algebraically:
m∠y° + m∠90° = m∠115°
y° + 90° = 115°
Subtract 90° from both sides:
y° + 90° - 90° = 115° - 90°
y° = 25°
Double-check:
Verify whether we have the correct value for y by solving for x:
Since the exterior angle, ∠115°, and ∠x° are supplements, then it means that:
m∠115° + m∠x° = 180°
115° + x° = 180°
Subtract 115° from both sides:
115°- 115° + x° = 180° - 115°
x = 65°
According to the Triangle Sum Theorem, the sum of the measures of the interior angles of a triangle is 180°.
Hence:
m∠x° + m∠y° + m∠90° = 180°
65° + 25° + 90° = 180°
180° = 180° (True statement).
Therefore, the correct answer is: y = 25°. This measure represents either one of the ∠y.