Q12 - Geometry

Question

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

• $\angle ADE$
  

Step-by-Step Solution

Answer

The angle $\angle ADE$ appears to be straight angle and it’s estimated measure is $(m\angle 5+m\angle 6+m\angle 7)$.

Step 1. Apply the definition of straight angle.

Straight angle is an angle which measures exactly $180°$.

Step 2. Description of step.

From the given figure, it can be observed that the $\angle ADE$ measures exactly, $180°$ therefore, $\angle ADE$ appears to be straight angle.

Step 3. Estimate the measure of ∠ADE

Clearly, $\angle ADE=\angle ADB+\angle BDC+\angle CDE$ wherein $\angle ADB=m\angle 5$, $\angle BDC=m\angle 6$ and $\angle CDE=m\angle 7$.

$\begin{array}{l}\angle ADE=m\angle 5+m\angle 6+m\angle 7\\ =180°\end{array}$

Therefore, the estimated measure of $\angle ADE=180°$.