Question

5)
6)
34
m
n
k
178
110
$y = 178\frac{1}{2}(x - 34)$
$356 = x - 34$
+34

Explanation:

Step1: Use the formula for the measure of an angle formed by a secant and a tangent

The formula is $\theta=\frac{1}{2}(m\overset{\frown}{major}-m\overset{\frown}{minor})$. Here, $\theta = 34^{\circ}$, $m\overset{\frown}{major}=x$, and $m\overset{\frown}{minor}=178^{\circ}$.

Step2: Substitute the values into the formula

We have $34=\frac{1}{2}(x - 178)$.

Step3: Solve the equation for $x$

Multiply both sides by 2: $34\times2=x - 178$. So, $68=x - 178$.

Step4: Isolate $x$

Add 178 to both sides: $x=68 + 178$.

Answer:

$x = 246^{\circ}$