Question

find the value of x in given figure​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

value of angle x is = 105 degree

step by step explanation:

• In the picture of your question, ∆ PRS is an isosceles triangle because the length of its two sides are same.
• ∆ PQR is also an isosceles triangle because the length of its two sides are also same.
• We know that an isosceles triangle has two equal sides and two equal angles , and the angle opposite to the one of the equal side of an isosceles triangle is equal to the angle opposite to the other equal side of the triangle and vice versa.
• we also know that the sum of all interior angles of any triangle , and the sum of all angles that are on any straight line are equal to 180 degree.

angle QPR + angle RPS + angle x is equal to 180 degree ( QPR + angle RPS + angle x = 180°) because sum of all the angles that are on any straight line is equal to 180 degree.

let's try to find the value of angle x.

angle QPR + angle RPS + angle x = 180 °

=>angle x = 180 ° - angle QPR - angle RPS

=>angle x = 180 ° - 35° - angle RPS

so, angle x = 180 ° - 35° - angle RPS

for finding the value of angle x we have to find the value of angle RPS

let's try to find the value of angle RPS.

(angle PRS + angle RSP )+ angle RPS = 180°

=>angle RPS = 180° - (70° + angle RSP)

for finding the value of angle RPS we have to find the value of angle RSP.

angle RSP is equal to to angle PRS because angle RSP is opposite to the one of the equal side of the isosceles triangle PRS , hence angle PRS is equal to 70 degree.

So,angle RPS = 180° - (70° + angle RSP)jt

=angle RPS = 180° - (70° + 70°)

=angle RPS = 180° -140°

=angle RPS = 40°

hence,angle x = 180 ° - 35° - angle RPS

=angle x = 180 ° - 35° - 40°

=angle x = 180 ° - 75°

=angle x =105°

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