Question

gles, g-j are rhombi, and k-l are squares. find each cord the number with the color. color the picture!
b find $m\angle p$ and $m\angle q$.
$m\angle p =$
number:
$m\angle q =$
color:

Explanation:

Step1: Use rhombus consecutive angles sum

In a rhombus, consecutive angles are supplementary, so their sum is $180^\circ$.
$$(14x + 6) + (5x + 3) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.
$$19x + 9 = 180$$
$$19x = 171$$
$$x = 9$$

Step3: Find $m\angle P$

$\angle P$ is congruent to $\angle R$ (opposite angles of rhombus are equal). Substitute $x=9$ into $\angle R$'s expression.
$$m\angle P = 5x + 3 = 5(9) + 3 = 48$$

Step4: Find $m\angle Q$

$\angle Q$ is congruent to $\angle S$ (opposite angles of rhombus are equal). Substitute $x=9$ into $\angle S$'s expression.
$$m\angle Q = 14x + 6 = 14(9) + 6 = 132$$

Answer:

$m\angle P = 48^\circ$
$m\angle Q = 132^\circ$