Here are the step-by-step solutions for each problem.
Q3. Find the missing exterior angle in this polygon
Step 1: Understand the rule.
For any convex polygon, if you add up all the exterior angles (the angles outside the shape), they always equal
$360^\circ$.
Step 2: Add the known exterior angles.
The image shows four exterior angles: $70^\circ$, $75^\circ$, $55^\circ$, and $85^\circ$.
$$70 + 75 + 55 + 85 = 285^\circ$$
Step 3: Subtract from the total to find the missing one.
$$360^\circ - 285^\circ = 75^\circ$$
Final Answer:
The missing exterior angle is
$75^\circ$.
***
Q4. Find interior angle x in this polygon
Step 1: Identify the type of polygon.
The shape has 4 sides, so it is a quadrilateral. The sum of the interior angles of any quadrilateral is always
$360^\circ$.
Step 2: Find the missing interior angles using the exterior angles.
An interior angle and its corresponding exterior angle form a straight line, meaning they add up to $180^\circ$.
* Top-right exterior is $70^\circ$, so the interior angle is: $180^\circ - 70^\circ = 110^\circ$.
* Bottom-left exterior is $96^\circ$, so the interior angle is: $180^\circ - 96^\circ = 84^\circ$.
Step 3: Set up the equation for the sum of interior angles.
We have three known interior angles ($90^\circ$, $110^\circ$, $84^\circ$) and one unknown angle ($x$).
$$90 + 110 + 84 + x = 360$$
Step 4: Solve for $x$.
First, add the known numbers:
$$90 + 110 + 84 = 284$$
Now subtract that sum from $360$:
$$x = 360 - 284$$
$$x = 76$$
Final Answer:
The interior angle $x$ is
$76^\circ$.
***
Q5. Part of a regular polygon is shown. The exterior angle is $24^\circ$. How many sides does it have?
Step 1: Use the exterior angle formula.
For a regular polygon, the number of sides ($n$) is found by dividing $360^\circ$ by the size of one exterior angle.
$$\text{Number of sides} = \frac{360}{\text{Exterior Angle}}$$
Step 2: Calculate.
$$\text{Number of sides} = \frac{360}{24}$$
$$360 \div 24 = 15$$
Final Answer:
It has
15 sides.
***
Q6. Part of a regular polygon is shown. The interior angle is $162^\circ$. How many sides does it have?
Step 1: Find the exterior angle first.
Since the interior and exterior angles add up to $180^\circ$:
$$\text{Exterior Angle} = 180^\circ - 162^\circ = 18^\circ$$
Step 2: Use the exterior angle formula to find the number of sides.
$$\text{Number of sides} = \frac{360}{\text{Exterior Angle}}$$
$$\text{Number of sides} = \frac{360}{18}$$
Step 3: Calculate.
$$360 \div 18 = 20$$
Final Answer:
It has
20 sides.
Parent Tip: Review the logic above to help your child master the concept of interior and exterior angles of polygons worksheet key.
