Sample response: The Smith family has 2 choices to make, color
and style. By the fundamental counting principle, the product of the
number of choices of color and style must equal 8. So, there could be 1
color and 8 style choices, 2 colors and 4 styles, 4 colors and 2 styles,
or 8 colors and 1 style.
Answer:
The option is C i.e 115°, 65°. proof is given below.
Step-by-step explanation:
Given:
ABCD is a quadrilateral.
m∠ A = 100 + 5x
m∠ B = 77 - 4y
m∠ C = 106 + 3x
m∠ D = 47 + 6y
To Prove:
ABCD is a parallelogram if opposing angles are congruent by finding the measures of angles.
m∠ A = m∠ C and
m∠ B = m∠ D
Proof:
ABCD is a quadrilateral and is a parallelogram if opposing angles are congruent.
∴ m∠ A = m∠ C
On substituting the given values we get
∴ 100 + 5x = 106 +3x
∴ 
m∠ A = 100 + 5x = 100 + 5 × 3 =100 + 15 = 115°
m∠ C = 106 + 3x = 106 + 3 ×3 =106 + 9 = 115°
∴ m∠ A = m∠ C = 115°
Similarly,
∴ m∠ B = m∠ D
77 - 4y = 47 + 6y
10y = 77 - 47
10y =30
∴
m∠ B = 77 - 4y =77 - 4 × 3 = 77 - 12 = 65°
m∠ D = 47 + 6y = 47 + 6 × 3 = 47 + 18 = 65°
∴ m∠ B = m∠ D = 65°
Therefore the option is C i.e 115°, 65°
Answer:
The triangle is obtuse, and isosceles.
Step-by-step explanation:
The triangle is obtuse because there is an angle above 90 degrees, which is 104 degrees. The triangle is also isosceles due to the two lines in the triangle which indicate that the size of each side are equal to each other. For a triangle to be isosceles, there have to be at least two sides equal to each other, and in this case the triangle has those two equal sides.
Answer:
Step-by-step explanation:
A.t.q,
2πr+2r=116 cm
2r(π+1)=116 cm
2r(22/7+1)=116 cm
2r(22+7/7)=116 cm
2r=116×7/29
2r=28 cm
r=28/2
r=14 cm
Thank you
Answer:
Step-by-step explanation:
<h3>Given </h3>
- Points A(-1,7) and B (11,-1)
<h3>To find</h3>
<h3>Solution</h3>
<u>Using midpoint formula</u>
- x = (-1 + 11)/2 = 10/2 = 5
- y = (7 -1)/2 = 6/2 = 3
Midpoint is (5, 3)
