Question

fill in the blanks with the missing angle numbers to complete the flow - char
∠fkd and ∠hrl are complementary; ∠wxb and ∠hrl are complementary; given
m∠fkd + m∠fill in 1 = 90°; m∠wxb + m∠hrl = 90° definition of complementary angles
m∠fkd + m∠hrl = m∠fill in 2 + m∠hrl transitive property of equality
m∠hrl = m∠fill in 3 reflexive property of equality
m∠fill in 4 = m∠wxb subtraction property of equality
∠fkd ≅ ∠wxb definition of congruence
fill in 1:
fill in 2:
fill in 3:
fill in 4:

Explanation:

Step1: Recall complementary - angle definition

Since $\angle FKD$ and $\angle HRL$ are complementary, $m\angle FKD + m\angle HRL=90^{\circ}$. Also, given $m\angle FKD + m\angle[\text{FILL IN 1}]=90^{\circ}$, by the definition of complementary angles, $\text{FILL IN 1}=\angle HRL$.

Step2: Use transitive property

We know $m\angle FKD + m\angle HRL=m\angle[\text{FILL IN 2}]+m\angle HRL$. By the transitive property of equality, if $a + c=b + c$, then $a = b$. So $\text{FILL IN 2}=\angle FKD$.

Step3: Apply reflexive property

The reflexive property of equality states that $m\angle HRL=m\angle HRL$, so $\text{FILL IN 3}=\angle HRL$.

Step4: Use subtraction property

Starting from $m\angle FKD + m\angle HRL=m\angle WXB + m\angle HRL$ (from previous steps), using the subtraction property of equality (subtract $m\angle HRL$ from both sides), we get $m\angle FKD=m\angle WXB$. So $\text{FILL IN 4}=\angle FKD$.

Answer:

FILL IN 1: $\angle HRL$
FILL IN 2: $\angle FKD$
FILL IN 3: $\angle HRL$
FILL IN 4: $\angle FKD$