Question

The ratio of the angle measures in a triangle $11:14:20$. How do you find the angle measures? Then classify the triangle by its angle measures?

Answer 1

Hint:We will start off by explaining the angles as some variables. Then we will be using the property of triangle, that the sum of all the angles of triangle is ${180^0}$. We have considered an unknown variable as $11x,14x\,$ and $20x$ to further simplify and evaluate the terms.

Complete step by step answer:
We will start off by considering the given ratios of angles as some unknown variables. Here, we will consider $x$ as the common factor for all the angles so that we can write the angles with the help of variables as $11x,14x\,$ and $20x$
So, now we will apply the property of triangle that the sum of all the angles of triangle is ${180^0}$.
$
11x + 14x\, + 20x = {180^0} \\
45x = {180^0} \\
x = {4^0} \\
$
Now that we have the value of the variable, we will evaluate the values of all the angles.
$
11x = 11(4) = {44^0} \\
14x = 14(4) = {56^0} \\
20x = 20(x) = {80^0} \\
$
Hence, the measures of the angles are ${44^0},{56^0},{80^0}$.
Now as all the angles are acute, this triangle is an acute angled triangle.
Additional Information:
Expression is a mathematical sentence which has numbers, variables, and operations and there is no equal sign. Simplify means to break down an expression to its simplest forms. Variable is a number that we don’t know, or which can change. Algebraic expressions are useful because they represent the value of an expression for all of the values a variable can take on.
Acute angled triangle is a triangle which has the measures of all its angles less than ${90^0}$

Note: While converting orders do not matter for addition and multiplication. But order is important for subtraction and division. Make sure that you read the statement twice before translating it to an expression. Pay extra attention to the statements where multiplication and division is involved. While evaluating the type of triangle, evaluate each angle of the triangle.