The question asks for the measure of the exterior angle at the right-angled vertex of a right triangle, given that one acute angle is $30^\circ$. Let's break this down:
Right Triangle Angle Properties
- A right triangle is defined as a triangle containing one angle that measures exactly $90^\circ$. This is the right-angled vertex.
- The sum of the interior angles in any triangle is always $180^\circ$.
- In a right triangle, the sum of the two acute angles must be $90^\circ$ ($180^\circ - 90^\circ = 90^\circ$).
Exterior Angle Calculation
- Identify the interior angle at the right-angled vertex: By definition, this is $90^\circ$.
- Use the supplementary angle property: An exterior angle and its adjacent interior angle form a linear pair, meaning they add up to $180^\circ$.
- Calculate the exterior angle: Exterior Angle = $180^\circ$ - Interior Angle at the right-angled vertex Exterior Angle = $180^\circ - 90^\circ$ Exterior Angle = $90^\circ$
The fact that one acute angle is $30^\circ$ (implying the other is $60^\circ$) is extra information not needed to find the exterior angle at the $90^\circ$ vertex itself.
Similar Questions
- When a transversal intersects two parallel lines, one of the alternate interior angles is 115°. What is the measure of the angle that lies opposite to it on the alternate interior side?
- At an intersection of two lines, two angles are vertically opposite. If one of the angles measures $45^\circ$, what is the measure of the other angle?
- Two angles are complementary. The measure of one angle is 10 degrees more than three times the measure of the other angle. What is the measure of the smaller angle?
Two parallel lines are intersected by a transversal. If a pair of corresponding angles is formed, and one of the angles measures 130°, what is the measure of the other angle?
- If the angle subtended by arc AB at the center is $140^\circ$, what is the reflex angle made by this arc at the center?
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