Q25. - Geometry

Question

Name a pair of congruent:

a. acute angles

b. right angles

c. obtuse angles

Step-by-Step Solution

Answer

1. A pair of congruent acute angles is $\left(\angle AOB,\angle AOB\right)$.
2. A pair of congruent right angles is  $\left(\angle AOC,\angle COH\right)$.
3. A pair of congruent obtuse angles is $\left(\angle AOG,\angle HOB\right)$.

a. Step 1 - Apply the definition of congruent angles

Congruent angles are the angles that have equal measures.

a. Step 2 - Apply the definition of acute angles

Acute angles are the angles which measures between $\mathbf{0}\mathbf{°}$ and $\mathbf{90}\mathbf{°}$.

a. Step 3 - Observe the figure and identify a pair of congruent acute angles

From the figure, it can be observe that $\angle AOB$ and $\angle HOG$ are both congruent and acute angles, that is, both measures   $20°$ and is less than $90°$.

Therefore, a pair of congruent acute angles is $\left(\angle AOB,\angle HOG\right)$.

b. Step 1 - Apply the definition of congruent angles

Congruent angles are the angles that have equal measures.

b. Step 2 - Apply the definition of right angle

Right angle is an angle which measures exactly $\mathbf{90}\mathbf{°}$.

b. Step 3 - Observe the figure and identify a pair of congruent right angles

From the figure, it can be observe that $\angle AOC$ and $\angle COH$ are both congruent and right angles, that is, both measures exactly $90°$.

Therefore, a pair of congruent right angles is $\left(\angle AOC,\angle COH\right)$.

c. Step 1 - Apply the definition of congruent angles

Congruent angles are the angles that have equal measures.

c. Step 2 - Apply the definition of obtuse angles

Obtuse angles are the angles which measures between $\mathbf{90}\mathbf{°}$ and $\mathbf{180}\mathbf{°}$.

c. Step 3 - Observe the figure and identify a pair of congruent obtuse angles

From the figure, it can be observe that $\angle AOG$ and $\angle HOB$ are both congruent  angles and obtuse angles that is, both measures $160°$ and are less than $180°$.

Therefore, a pair of congruent obtuse angles is $\left(\angle AOG,\angle HOB\right)$.