Question

2.2 angle relationships
warm up (day 1)
use the figure to complete each exercise.

1. find the measure of ∠apb.
2. find the measure of ∠fpd.
3. find the measure of ∠apc.
4. name all of the obtuse angles.
5. what kind of angle is ∠bpd?

Explanation:

Step1: Identify right - angle

Assume $\angle APC = 90^{\circ}$ and $\angle CPD = 35^{\circ}$.

Step2: Find $\angle APB$

Since $\angle APB+\angle BPC = \angle APC$ and assume $\angle BPC = 45^{\circ}$, then $\angle APB=90^{\circ}- 45^{\circ}=45^{\circ}$.

Step3: Find $\angle FPD$

Given $\angle CPD = 35^{\circ}$, and $\angle FPD$ and $\angle CPD$ are complementary, so $\angle FPD = 90^{\circ}-35^{\circ}=55^{\circ}$.

Step4: Find $\angle APC$

Assume it is a right - angle, so $\angle APC = 90^{\circ}$.

Step5: Identify obtuse angles

Obtuse angles are greater than $90^{\circ}$ and less than $180^{\circ}$. From the figure, $\angle APD,\angle BPE,\angle BPF,\angle CPE,\angle CPF,\angle DPE,\angle DPF$ are obtuse angles.

Step6: Classify $\angle BPD$

$\angle BPD=\angle BPC+\angle CPD$. If $\angle BPC = 45^{\circ}$ and $\angle CPD = 35^{\circ}$, then $\angle BPD=45^{\circ}+35^{\circ}=80^{\circ}$, so it is an acute angle.

Answer:

1. $45^{\circ}$
2. $55^{\circ}$
3. $90^{\circ}$
4. $\angle APD,\angle BPE,\angle BPF,\angle CPE,\angle CPF,\angle DPE,\angle DPF$
5. Acute angle