m ∠ACB = 28
<u>Step-by-step explanation:</u>
In any circle, an inscribed angle measure is exactly the half of the central angle measure with the same arc that is intercepted.
Here the angle AOB is the central angle measure then the measure of the angle ACB is half of the angle AOB.
m<ACB = × m<AOB
=
= 28
So the measure of angle ACB is 28 degrees.
I'm guessing that you know about 45-45-90 and 30-60-90 triangles.
In 45-45-90 triangles, the legs are in a ratio such that the hypotenuse is times the legs.
In 30-60-90 triangles, the legs are in a ratio of 1::2
In the picture given we have been given a value of the side of the 45-45-90 triangle. We can deduce that the value of the hypotenuse is 9 because of the ratio of the sides of a 45-45-90 triangle.
The 30-60-90 triangle shares the same hypotenuse, and so we now know a value of one of its sides as well. The ratio of the side of value 'x' and the hypotenuse is : 2
We can create an equation to solve for x using these ratios:
=
Cross multiply:
2x = 9
x =
Option C
Student is wrong An exterior angle of a triangle can be adjacent to the right angle of a right triangle, so an exterior angle can be a right angle.
<h3>What is exterior angle?</h3>The Exterior Angle is the angle between any side of a shape, and a line extended from the next side.
The student make an error he states that the exterior angle of a triangle can never be a right angle.
The correct answer will be option D that is An exterior angle of a triangle can be adjacent to the right angle of a right triangle, so an exterior angle can be a right angle.I have also attached the diagram of the triangle for better understanding.
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