Question

find the value of x in the given figure ​

Answer 1

Answer:

72°

because T =90

P=30

90+30=120

another angle i.e congruent to x is 60 as (180-120 =60 )

x is congruent to it so it is also 60

48 +60=108

180-108=72

Answer 2

in figure, it is clearly shown that, QT is perpendicular on PR,

so, angle PTQ = 90°

let PS and QT intersect at A

from ∆PAT,

angle PAT + angle APT + angle PTA = 180°

⇒angle PAT + 30° + 90° = 180°

⇒angle PAT = 180° - 120° = 60°

it is clear that, angle PAT = angle QAS

from ∆QAS,

angle SQA + angle QAS + angle ASQ = 180°

⇒48° + 60° + x = 180°

⇒108° + x = 180°

⇒x = 180° - 108° = 72°

hence, x = 72°