Question

In the fig. PQ||TS, reflex ZQRS = 300° and x - y =
30°, find the measure of y?​

Answer 1

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Answer 2

Answer:

Measure of y is 15° ( option 2 )

Step-by-step explanation:

• In context to the given question, we have to find that the measure of "y"
• given that

1. PQ||TS,
2. Reflex ∠QRS = 300°
3. x - y = 30° [ eq. a ]

we know that,

By the rule of 360°

⇒ Reflex ∠QRS +∠QRS = 360°

⇒ 300° +∠QRS = 360°

⇒ ∠QRS = 360° - 300° [ by transposing method]

⇒ ∠QRS = 60°

Now as per the figure;

In Δ QRS

we know that ,

PQ||TS , Therefore, Line QS will be perpendicular to PQ and TS

∠ RQS = 90°- x
∠QRS = 60 °
∠RSQ = 90 °- y

By applying the angle sum property of triangle ;

∠ RQS + ∠QRS +∠RSQ = 180°

By putting the values of Angles known

90°- x + 60° + 90°-y = 180°

240 ° -x -y = 180°

x + y = 240° - 180°

x + y = 60° [eq. b ]

By subtracting eq. [ b] from [ a]

we get,

x + y - [ x - y ]= 60° - 30°

x + y -x + y = 30°

2y = 30°

y = 15°

Therefore, Measure of y is 15° ( option 2 )