Use the image to answer the question.
An illustration shows a triangle with a 90 degree angle at the top vertex. The interior angle of the left vertex is labeled x. A line extending outward from the right vertex forms an exterior angle of 152 degrees.
Find angle x
.
(1 point)
Responses
118°
118 degrees
62°
62 degrees
28°
28 degrees
90°
90 degrees
The sum of the interior angles of a triangle is always 180 degrees.
Since we know one angle is 90 degrees and the exterior angle at the right vertex is 152 degrees, we can find angle x by subtracting these two angles from 180 degrees.
180 - 90 - 152 = -62
Since angles cannot be negative, we can conclude that angle x is 62 degrees.
Therefore, the correct answer is:
62°
62 degrees
To find angle x, we can use the fact that the sum of the interior angles of a triangle is always 180 degrees.
Given that one of the interior angles is a right angle (90 degrees) and the exterior angle is 152 degrees, we can solve for angle x.
Since the exterior angle is the sum of the two remote interior angles, we can subtract 90 degrees from 152 degrees to find the measure of angle x.
152 degrees - 90 degrees = 62 degrees
Therefore, angle x is 62 degrees.
To find angle x, we need to use the properties of triangles and their angles.
From the given information, we know that the triangle has a 90-degree angle at the top vertex and an exterior angle of 152 degrees at the right vertex.
The sum of the measures of the interior angles in any triangle is always 180 degrees. So, we can subtract the given exterior angle (152 degrees) from 180 degrees to find the measure of the interior angle at the right vertex.
180 degrees - 152 degrees = 28 degrees
Now, we have found the measure of the interior angle at the right vertex, which is 28 degrees.
Since the sum of the angles in a triangle is always 180 degrees, we can find angle x by subtracting the measures of the two known angles from 180 degrees.
180 degrees - 90 degrees - 28 degrees = 62 degrees
Therefore, angle x is 62 degrees.