find the value of x and y in following figure
Answers
Step-by-step explanation:
Hint: We will use the angle sum property of triangles to solve this question. It is stated as “The Angle sum property of the triangle states that the sum of interior angles of a triangle is 180°”.
Complete step-by-step solution -
We are given the figure as,
hint - We have to find the value of x and y.
We have to find the value of x and y.We will use the angle sum property of the triangle to solve this question.
We have to find the value of x and y.We will use the angle sum property of the triangle to solve this question.The Angle sum property of a triangle states that the sum of interior angles of a triangle is 180°.
We have to find the value of x and y.We will use the angle sum property of the triangle to solve this question.The Angle sum property of a triangle states that the sum of interior angles of a triangle is 180°.Observing the given triangle PQR, we see that there are 2 triangles PSR and triangle PSQ.
We have to find the value of x and y.We will use the angle sum property of the triangle to solve this question.The Angle sum property of a triangle states that the sum of interior angles of a triangle is 180°.Observing the given triangle PQR, we see that there are 2 triangles PSR and triangle PSQ.Given that the angle PSR is 90 degrees and because QSR is the line, therefore, the angle QSR would be 180.
Then we get the value of angle PSQ = 180-90 = 90.
Hence, we obtained the angle PSQ and PSR are both 900900.
Now we will use angle sum property of triangle to solve further which is stated as,
The Angle sum property of a triangle states that the sum of interior angles of a triangle is 180°.
Consider ΔPSR ,ΔPSR,
Applying angle sum property of triangle, we get,
∠P+∠S+∠R=1800∠P+∠S+∠R=1800
Substituting the value of angle P as 400400, angle S as 900900 and angle R as y we get,
∠P+∠S+∠R=1800
⇒400+900+y=1800
⇒1300+y=1800
⇒y=1800−1300
⇒y=500∠P+∠S+∠R=1800
⇒400+900+y=1800
⇒1300+y=1800
⇒y=1800−1300
⇒y=500
Therefore, we get the value of y as y = 500500.
Similarly, applying the angle sum property of triangle in ΔPSQΔPSQ, we get,
∠P+∠S+∠Q=1800∠P+∠S+∠Q=1800
Substituting the value of angle Q as 600600, angle P as x and angle S as 900900, we get,
∠P+∠S+∠Q=1800
⇒600+900+x=1800
⇒1500+x=1800
⇒x=1800−1500
⇒x=300∠P+∠S+∠Q=1800
⇒600+900+x=1800
⇒1500+x=1800
⇒x=1800−1500
⇒x=300
Therefore, we got the value of x as x = 300300.
So, we get the value of x = 300300 and y = 500500.
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Answer:
x=300
y=500
Step-by-step explanation:
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