Question

pqrst ~ dcbae. what are ( mangle p ) and ( mangle b )?

Explanation:

Step1: Use similarity of polygons

Similar polygons have congruent corresponding angles. For $PQRST \sim DCBAE$, $\angle P$ corresponds to $\angle D$, and $\angle B$ corresponds to $\angle Q$.

Step2: Find $m\angle P$

$\angle P$ matches $\angle D$, so $m\angle P = m\angle D = 84^\circ$.

Step3: Calculate sum of pentagon angles

Sum of interior angles of a pentagon: $(5-2)\times180^\circ = 540^\circ$.

Step4: Find $m\angle Q$ (for $m\angle B$)

Calculate $m\angle Q$ using the sum:
$m\angle Q = 540^\circ - (73^\circ + 128^\circ + 131^\circ + 84^\circ)$
$m\angle Q = 540^\circ - 416^\circ = 124^\circ$
Since $\angle B$ corresponds to $\angle Q$, $m\angle B = 124^\circ$.

Answer:

$m\angle P = 84^\circ$
$m\angle B = 124^\circ$