Mrs. Rodriquez has 24 students in her class. Ten of the students are boys. Jeff claims that the ratio of boys to girls in this c
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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:
Image below
Step-by-step explanation:
<em>Given: Side lengths of a right triangle 3,4 and 5 units. </em>
<em> To draw: A right triangle with the given side length. </em>
<em> Solution: </em>
<em> We know, in a right angle triangle hypotenuse is the longest side and satisfying Pythagoras theorem. </em>
<em> From the given side length, </em>
<em> Hypotenuse = 5 unit </em>
<em> We can take any of the base and perpendicular. </em>
<em> Let, Base = 3 unit </em>
<em> Perpendicular = 4 unit. </em>
<em> It a right-angle triangle with a hypotenuse 5 unit. </em>
<em> Now we draw a right angle triangle taking in the first 3 base and 4 perpendicular and second 3 perpendicular and 4 bases.</em>
