Question

△ryb is shown where
$m\angle hyb = (8d + 9.5)^circ$
$m\angle bry = 29.7^circ$
$m\angle mbr = (4d - 5)^circ$
what is the value of d?
$d = $ type your answer...

Explanation:

Step1: Identify exterior angle relationships

$\angle HYB$ is an exterior angle of $\triangle RYB$, so $m\angle HYB = m\angle BRY + m\angle RBY$.
$\angle MBR$ and $\angle RBY$ are supplementary, so $m\angle RBY = 180^\circ - (4d - 5)^\circ$.

Step2: Substitute into exterior angle formula

$$(8d + 9.5) = 29.7 + [180 - (4d - 5)]$$

Step3: Simplify the right-hand side

$$8d + 9.5 = 29.7 + 180 - 4d + 5$$
$$8d + 9.5 = 214.7 - 4d$$

Step4: Isolate terms with $d$

$$8d + 4d = 214.7 - 9.5$$
$$12d = 205.2$$

Step5: Solve for $d$

$$d = \frac{205.2}{12}$$

Answer:

$17.1$