Question

there is a circle, and a triangle outside the circle. the circle has an arc of 74° and an arc of 86°. the angle of the triangle is (4x + 13)°. we need to find the value of x or solve related problems.

Explanation:

Step1: Recall external secant angle formula

The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs.

Step2: Substitute given values

$$4x + 13 = \frac{1}{2}(86 - 74)$$

Step3: Calculate right-hand side

$$4x + 13 = \frac{1}{2}(12) = 6$$

Step4: Solve for x

$$4x = 6 - 13 = -7$$
$$x = \frac{-7}{4}$$

Answer:

$x = -\frac{7}{4}$