Question

In the given figure line XY and MN intersect at O .If angle POY =90° and a:b= 1:4 find c.

Answer 1

Answer:

108°

Step-by-step explanation:

a:b = 1:4 means 5x = 90° (<poy + <pox = 180°)

so, x = 18°

Thus, <b = 18°×4= 72°

Again, <b + <c = 180°

Thus, <c = 180° - 72° = 108°

hope this will help you

Answer 2

Answer:

The measure of ∠c is 108°.

Step-by-step explanation:

XY and MN are strianght lines.

∠XOM, ∠MOP and ∠POY are on the line XY. This means their sum is 180°.

• ∠POY = 90°
• ∠a : ∠b = 1 : 4

Consider angle ∠a and ∠b as y and 4y respectively.

$\longrightarrow$ ∠POY + ∠a + ∠b = 180°

$\longrightarrow$ 90 + y + 4y = 180°

$\longrightarrow$ 90 + 5y = 180°

$\longrightarrow$ 5y = 180° - 90°

$\longrightarrow$ 5y = 90°

$\longrightarrow$ y = 90/5

$\longrightarrow$ y = 18°

So,

$\longrightarrow$ ∠a = 18°

• ∠b = 4y

$\longrightarrow$ ∠b = 4(18)

$\longrightarrow$ ∠b = 72°

On straight line MN, ∠b and ∠c form linear pair. Their sum is 180°

$\longrightarrow$ ∠b + ∠c = 180°

$\longrightarrow$ ∠c + 72° = 180°

$\longrightarrow$ ∠c = 180° - 72°

$\longrightarrow$ ∠c = 108°

Therefore, the measure of ∠c is 108°.