Q11 - Geometry

Question

State whether the angle appears to be acute, right, obtuse, or straight. Then estimate its measure.

• $\angle ADC$
  

Step-by-Step Solution

Answer

The angle $\angle ADC$ appears to be obtuse angle and it’s estimated measure is $(m\angle 6+m\angle 5)$.

Step 1. Apply the definition of acute angle

Obtuse angle is an angle which measures between $90°$ to $180°$.

Step 2. Description of step

From the given figure, it can be observed that the $\angle ADC$ measures between $90°$ to $180°$ therefore, $\angle ADC$ appears to be obtuse angle.

Step 3. Estimate the measure of ∠ADC

Clearly, $\angle ADC=\angle ADB+\angle BDC$ wherein $\angle ADB=m\angle 5$ and $\angle BDC=m\angle 6$. 

Therefore, $\angle ADC=m\angle 6+m\angle 5$.