The problem asks to identify the type of angle for the following angle measurements: a) $68^\circ$ b) $215^\circ$ c) $91^\circ$ d) $32^\circ$ e) $180^\circ$ f) $89^\circ$ g) $195^\circ$ h) $265^\circ$ i) $90^\circ$

1. Problem Description

The problem asks to identify the type of angle for the following angle measurements:

a) $68^\circ$

b) $215^\circ$

c) $91^\circ$

d) $32^\circ$

e) $180^\circ$

f) $89^\circ$

g) $195^\circ$

h) $265^\circ$

i) $90^\circ$

2. Solution Steps

We need to classify each angle based on its measure:

- Acute Angle: An angle that measures greater than $0^\circ$ and less than $90^\circ$. ($0^\circ < \theta < 90^\circ$)

- Right Angle: An angle that measures exactly $90^\circ$. ($\theta = 90^\circ$)

- Obtuse Angle: An angle that measures greater than $90^\circ$ and less than $180^\circ$. ($90^\circ < \theta < 180^\circ$)

- Straight Angle: An angle that measures exactly $180^\circ$. ($\theta = 180^\circ$)

- Reflex Angle: An angle that measures greater than $180^\circ$ and less than $360^\circ$. ($180^\circ < \theta < 360^\circ$)

a) $68^\circ$: Since $0^\circ < 68^\circ < 90^\circ$, it is an acute angle.

b) $215^\circ$: Since $180^\circ < 215^\circ < 360^\circ$, it is a reflex angle.

c) $91^\circ$: Since $90^\circ < 91^\circ < 180^\circ$, it is an obtuse angle.

d) $32^\circ$: Since $0^\circ < 32^\circ < 90^\circ$, it is an acute angle.

e) $180^\circ$: It is a straight angle.

f) $89^\circ$: Since $0^\circ < 89^\circ < 90^\circ$, it is an acute angle.

g) $195^\circ$: Since $180^\circ < 195^\circ < 360^\circ$, it is a reflex angle.

h) $265^\circ$: Since $180^\circ < 265^\circ < 360^\circ$, it is a reflex angle.

i) $90^\circ$: It is a right angle.

3. Final Answer

a) Acute Angle

b) Reflex Angle

c) Obtuse Angle

d) Acute Angle

e) Straight Angle

f) Acute Angle

g) Reflex Angle

h) Reflex Angle

i) Right Angle