Question

The angles of a triangle are arranged in ascending order of their magnitude. If the difference between two consecutive angle it ${10^ \circ }$, find the three angles

Answer 1

Hint : Such questions apply the properties of triangles in this question, the theorem stating” sum of all angles in a triangle is 180” .

Complete step-by-step answer:
Let us first extract the data given in the question and put it in a mathematical from. The question
Says that between two consecutive angle the difference is of ${10^ \circ }.$
Let its consider one angle as $'x'$ , then the next consecutive angle will be $'x + 10'$ and the last angle will be $'x + 20'.$
So, the three angle are $x,x + 10\;{\text{and}}\;x + 20.$
According to the theorem stated above in the hint,
We can say that,
$x + \left( {x + 10} \right) + \left( {x + 20} \right) = {180^ \circ }$
$ \Rightarrow 3x + 30 = {180^ \circ }$
$3x = 180 - 30$
$3x = 150$
$x = \dfrac{{{1}{5}{{{0}}^{{{}^ \circ }}}}}{{{3}}}$
$x = {50^ \circ }$
If one angle $x = {50^ \circ }$, then other angles will be ${60^{ \circ \;}}\;\& \;\;{70^ \circ }$ respectively $\left( {\because x + 10\;\& \;x + 20\;} \right).$

Note :In such types of questions basic properties of triangles are sufficient to extract the answer we should be very firm basics so that you won't struggle much in these questions.