Question

the figure shows a regular Pentagon and a regular hexagon put together. How much is PQR ?​

Answer 1

Answer:

Hey there!

The measure of angle PQR is 132 degrees.

Step-by-step explanation:

Question: The figure shows a regular Pentagon and a regular hexagon put together. How much is angle PQR?​

Previous Knowledge:

• Pentagon sides(n) = 5
• Hexagon sides (n)= 6

Formula to find one interior angle of a regular polygon = $\frac{(n-2)180 }{n}$

Solution:

One interior angle of a pentagon (n= 5)

$\frac{(5-2) 180}{5}\\ \\\\= \frac{3 (180)}{5}\\\\= \frac{540}{5}\\ \\=108degrees$

One interior angle of a hexagon(n=6)

$\frac{(6-2)180}{6} \\\\= \frac{4(180)}{6}\\\\= 4(30)\\\\= 120 degrees$  

The adjacent angle of measure 120 degrees = 180 - 120 = 60degrees

Similarly,  the adjacent angle of measure 108 degrees = 180 -108 = 72 degrees.

From the figure, The exterior angle PQR = sum of the adjacent angles

= (60 + 72)degrees

= 132 degrees

Hence, the answer is 132 degrees.

Thanks!

Answer 2

Given: The figure shows a regular Pentagon and a regular hexagon put together.

To find: The measure of PQR.

Solution:

A regular hexagon has its interior angle equal to 120°and a regular pentagon has its internal angle equal to 108°. Hence, at point Q, the hexagon makes 120°, the pentagon makes 108° and the angle PQR is to be calculated. The sum of these three angles would result to give a 360° as it would make a complete circle.

$120 + 108 + \angle PQR = 360$

$\angle PQR = 132$

Therefore, the measure of PQR is 132°.