Question

Calculate the value of the largest angle in the triangle above.

A. ${120^ \circ }$
B. ${115^ \circ }$
C. ${110^ \circ }$
D. ${105^ \circ }$

Answer 1

Hint: In the above question, we have given all the values of an obtuse angled triangle. Now, we know that in the obtuse angle triangle, there is an angle which is greater than ${90^ \circ }$ . Now, we will use the angle sum property to calculate the variable given in the question. Now, we know that angle sum property says that the total of all the angles of a triangle is ${180^ \circ }$ . Now, by adding all the angles and equating them to ${180^ \circ }$ , will provide us the correct answer.

Complete step-by-step answer:

In the diagram, we can see that there are the values of all the angles.
These angles are $2x,3x$ and $7x$ .
Now, we will use angle sum property,
We know the sum of all the angles of a triangle is ${180^ \circ }$ .
Now, by equating the total of the angles to ${180^ \circ }$
We get that,
$ \Rightarrow 3x + 2x + 7x = 180$
Now, on simplifying,
$
   \Rightarrow 3x + 2x + 7x = 180 \\
   \Rightarrow 12x = 180 \\
   \Rightarrow x = 15 \\
 $
Now, we have to find the value of the largest angle,
So, the values of all the angles are $2 \times {15^ \circ } = {30^ \circ },3 \times {15^ \circ } = {45^ \circ },7 \times {15^ \circ } = {105^ \circ }$
Hence, the measure of all the angles are ${30^ \circ },{45^ \circ },{105^ \circ }$
Hence, the value of the largest angle is ${105^ \circ }$ .

Hence, the correct option is D.

Additional Information: We have used the angle sum property here. Angle sum property states that the sum of all the angles of a triangle must be equal to ${180^ \circ }$ .

Note:
In the above question we have used angle sum property, as it is the easiest way to solve these kinds of problems. Now, after finding the value of the variable in the question, we have evaluated the values of all the angles and then we have got the largest angle among them. always remember properties of triangles or whatever figure you are dealing with, it always saves your time and less errors.