Question

in the given figure, if PQR +QPR + QOS = 312°, FIND ALL THE FOUR ANGLES​

Answer 1

Step-by-step explanation:

In the given figure,

∠POS = ∠ROQ...........(Vertically Opposite Angles)

∠POR = ∠SOQ...........(Vertically Opposite Angles)

Now,

∠POR + ∠QOR + ∠QOS = 312°

(∠POR + ∠QOR) + ∠QOS = 312° ..........(∠POR and ∠QOR forms linear pair)

180 + ∠QOS = 312°

∠QOS = 312 - 180

∠QOS = 132

So, ∠QOS = ∠POR = 132°

Now,

∠POR + QOR + QOS = 312°

132 + ∠QOR + 132 = 312°

∠QOR + 264 = 312°

∠QOR = 312 - 264

∠QOR = 48

So, ∠POS = ∠QOR = 48°

Therefore, measure of angles are:

Therefore, measure of angles are:∠POR = 132°

Therefore, measure of angles are:∠POR = 132°∠QOR = 48°

Therefore, measure of angles are:∠POR = 132°∠QOR = 48°∠QOS = 132°

Therefore, measure of angles are:∠POR = 132°∠QOR = 48°∠QOS = 132°∠POS = 48°