Help me find the missing angles

Mathematics

1 answer:

Keith_Richards [23]3 years ago

8 0

Answer:

b) 105°

d) 130°

Step-by-step explanation:

An external angle has the same measure as the sum of the remote internal angles.

b) ? = 25° +80° = 105°

d) ? = 35° +95° = 130°

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This should be fairly obvious if you consider that the adjacent internal angle together with the external angle totals 180°, and the adjacent internal angle together with the other two internal angles totals 180°.

If the two "remote" angles are A and B, and the adjacent internal angle is C, then we have in symbols ...

A + B + C = 180° = ? + C

If we subtract C, then we find ...

A + B = ? . . . . . . the fact we used above

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taurus [48]

Answer:

$x^2 - 2x + 10$ , option B

Step-by-step explanation:

Complex numbers:

The most important relation that involves complex numbers is given by:

$i^2 = -1$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

The solutions are:

$x_1 = 1 - 3i, x_2 = 1 + 3i$

We have to find the polynomial. All option have $a = 1$ . So

$(x - (1 - 3i))(x - (1 + 3i)) = x^2 - x(1 + 3i) - x(1 - 3i) + (1 - 3i)(1 + 3i) = x^2 - x -3ix - x + 3ix + 1^2 - (3i^2) = x^2 - 2x + 1 - 9i^2 = x^2 - 2x + 1 - 9(-1) = x^2 - 2x + 10$