For instance, suppose there is a triangle in which two angles measure 70 and 84 degrees respectively and we are asked to calculate the third angle. These kinds of problems have the measures of indicated angles.
Let us learn how to find the indicated angle measure through the following examples:
Considering the above problem of triangle whose two of the angles have measures $70^0$ and $84^0$, calculate the measure of third angle?
To calculate the third angle, we can use theorem of angle sum of triangle. According to this theorem, sum of all angles is equals to $180^0$. In our triangle $\bigtriangleup$ABC, we can write:
$\angle$ABC + $\angle$ACB + $\angle$BAC = $180^0$
Substituting the values of the given angles, we get measure of indicated angle as:
70 + $\angle$ACB + 84 = $180^0$
or $\angle$ACB = $180^0 - (154)$
or $\angle$ACB = 260.
Suppose we have a quadrilateral with three of its angles as $60^0, 120^0$ and $80^0$ as shown in the figure.
Find the missing angle value.
Sum of all angles in a quadrilateral is $360^0$. Using this theorem, we can write as follows:
$\angle$DCB + $\angle$ADC + $\angle$DAC + $\angle$ABC = $360^0$ ............. (1)
Substituting the values of known angles in above equation, we get:
60 + 120 + 80 + $\angle$DBC = $360^0$
or $\angle$DBC = $360 - (260^0)$
or $\angle$DBC = $100^0$
We can verify our result by substituting values of all angles in equation (1).