Answer:
1. Which angles are adjacent.
CBX and FBC
Step-by-step explanation:
Okay so an adjacent angle is two angles with a common side. This means angles CBX and FBC are adjacent because they have the common side of "BC/CB"
Answer
2. Find the sum of the interior angles of a nonagon
1,260
Step-by-step explanation:
A nonagon is a 9 sided polygon with angles of 140. It wants the sum of all the angles. Since it has 9 sides, it has 9 angles. Now you can add 140, 9 times, or do 140 x 9. This gets you 1,260.
Answer
3. The measure of angle 3 is 101. find the measure of angle 4.
79
Step-by-step explanation.
Okay so both angles are against the same intersecting line, this means their sum must be 180. All we have to do here is subtract 180 and 101. this gets us 79.
Answer
4. Find the measure of each interior angle of a regular polygon with 12 sides.
1800
Step-by-step explanation.
Okay so a 12 sided regular polygon is a dodecagon. This has 12 angles with the degree of 150. This means 150 x 12 just like the 2nd question about nonagons. So 150 x 12 is 1800
Now that i've showed you how to do the first 4 you can apply the rest of the information on your own for 5 and the rest of the test.
1. [tex]\boxed{\angle CBX{\text{ and }}\angle FBC}[/tex] are adjacent angles.
2. The sum of the interior angles of a nonagon is [tex]\boxed{{{1260}^ \circ }}.[/tex]
3. The measure of angle4 is [tex]\boxed{{{79}^ \circ }}.[/tex]
4. The sum of the interior angles of a regular polygon is [tex]\boxed{{{1800}^ \circ }}.[/tex]
5.the measure of the missing angle of a pentagon is [tex]\boxed{{{115}^ \circ }}.[/tex]
Further Explanation:
The formula for the sum of angles of a polygon can be expressed as follows,
[tex]\boxed{{\text{Sum of angles}} = \left( {n - 2} \right) \times {{180}^ \circ }}[/tex]
Explanation:
Part (1)
Adjacent angles are those angles that have common line and common vertex.
[tex]\angle CBX{\text{ and }}\angle FBC[/tex] has the common vertex B and common line BC.
Therefore, [tex]\angle CBX{\text{ and }}\angle FBC[/tex] are adjacent angles.
Part (2)
Nonagon has 9 sides.
The sum of all the interior angles can be obtained as follows,
[tex]\begin{aligned}{\text{Sum of angles}} &= \left( {9 - 2} \right) \times 180\\&= 7 \times 180\\&= 1260\\\end{aligned}[/tex]
Part (3)
The measure of angle4 can be obtained as follows,
[tex]\begin{aligned}\angle 3 + \angle 4 &= {180^ \circ }\\{101^ \circ } + \angle 4 &= {180^ \circ }\\\angle 4 &= {180^ \circ } - {101^ \circ }\\\angle 4 &= {79^ \circ }\\\end{aligned}[/tex]
Part (4)
The polygonhas 12 sides.
The sum of all the interior angles can be obtained as follows,
[tex]\begin{aligned}{\text{Sum of angles}} &= \left( {12 - 2} \right) \times 180\\&= 10 \times 180\\&= 1800\\\end{aligned}[/tex]
Part (5)
The missing angle can be obtained as follows,
[tex]\begin{aligned}{85^ \circ } + {110^ \circ } + {135^ \circ } + {95^ \circ } + x &= {540^ \circ }\\{425^ \circ } + x &= {540^ \circ }\\x &= {540^ \circ } - {425^ \circ }\\x&= {115^ \circ }\\\end{aligned}[/tex]
Learn more:
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Angles
Keywords: vertical angle, opposite angle, angles, alternate angles, linear pair, corresponding angles, adjacent angle, missing angle, n, 12 sides.
