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
- 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?
- 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?
- 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?
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?
- 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?
Important Questions from Lines and Angles
Two parallel lines are intersected by a transversal, the corresponding angles are:
If l, m, n are lines such that, l is parallel to n and m is parallel to n, then, ______
There are three points P, Q and R on a straight line such that PQ : QR = 3 : 5. If n is the number of possible values of PQ : PR, then what is n equal to ?
Two cars start from a point at the same time and travel on two different roads at right angles to each other. Their speed is 18 km/h and 72 km/h respectively. What will be the distance between them after 6 seconds?
If angles of a triangle are in the ration of 2 : 3 : 4, then the measure of the smallest angle is:
