Answer :
The value of x in the triangle is 80°.
How to find the value of x in the triangle?
Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Let the third angle in triangle be y. Thus:
y = 180 - 115 (angle on a straight line)
y = 65°
Also:
35 + x + y = 180 (angle in a triangle)
35 + x + 65 = 180
x = 180 - 65 - 35
x = 80°
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Without sufficient context or additional information about the relationship between the angle 35° and the angle x, it is not possible to accurately find the value of x. The question seems to involve the use of trigonometric identities and inverse trigonometric functions to find angles or solve equations.
The question appears to be asking to find the value of an angle x in Mathematics, specifically involving trigonometric identities or equations. Unfortunately, the provided information is insufficient to determine the specific relationship or figure in question, which means that without additional context, solving for x is not possible. However, it refers to using the trigonometric identity sin(90° - x) = cos x, which is a fundamental identity in trigonometry explaining the complementary relationship between the sine and cosine of complementary angles. Moreover, it mentions finding solutions to equations of the form f(x) = 0 and inverse trigonometric functions, suggesting that a deeper level of problem-solving in trigonometry is being exercised.
