Question

Find the measure of $2\angle A+4\angle B$ if$\angle A=12°52\text{'}39"$and$\angle B=15°24\text{'}33".$

Answer 1

Finding the measure of $2\angle A+4\angle B$ :

Given that,

$\angle A=12°52\text{'}39"$

$\angle B=15°24\text{'}33"$

We have to find the value of $2\angle A+4\angle B$

Puting the values of $\angle A$and $\angle B$, we get

$\begin{array}{rcl}& & 2\times \left(12°52\text{'}39"\right)+4\times \left(15°24\text{'}33\text{'}\text{'}\right)\\ & & 2\times \left(12°+52\text{'}+39\text{'}\text{'}\right)+4\times \left(15°+24\text{'}+33\text{'}\text{'}\right)\\ & & 24°+104\text{'}+78\text{'}\text{'}+60°+96\text{'}+132\text{'}\text{'}\\ & & 84°+200\text{'}+210\text{'}\text{'}\\ & & \begin{array}{rcl}& & 84°+200\text{'}+180\text{'}\text{'}+30\text{'}\text{'}\end{array}\\ & & 84°+200\text{'}+3\text{'}+30\text{'}\text{'}\left[1\text{'}=60\text{'}\text{'}\right]\\ & & 84°+203\text{'}+30\text{'}\text{'}\\ & & \begin{array}{rcl}& & 84°+180\text{'}+23\text{'}+30\text{'}\text{'}\end{array}\\ & & 84°+3°+23\text{'}+30\text{'}\text{'}\left[1°=60\text{'}\right]\\ & & 87°23\text{'}30\text{'}\text{'}\end{array}$

Hence, $87°23\text{'}30\text{'}\text{'}$ is the required answer.