It is 9. You have to add 33y, then divide by 11 and you get x = 3y + 9
Answer: C. Definition of an Altitude
Step-by-step explanation:
Given: In triangle MNO shown below, segment NP is an altitude from the right angle.
Let ∠MNP=x
Then ∠PNO=90°-x
Therefore in triangle MNO,
∠MPN=∠NPO =90° [by definition of Altitude]
[Definition of altitude : A line which passes through a vertex of a triangle, and joins the opposite side forming right angles. ]
Now using angle sum property in ΔMNP
∠MNP+∠MPN+∠PMN=180°
⇒x+90°+∠PMN=180°
⇒∠PMN=180°-90°-x
⇒∠PMN=90°-x
Now, in ΔMNO and ΔPNO
∠PMN=∠PNO=90°-x
and ∠MPN=∠NPO =90° [by definition of altitude]
Therefore by AA similarity postulate, we have
ΔMNO ≈ ΔPNO
Think of the entire population of 6th graders here. 3/7 are boys and 4/7 are girls. 5/8 of these boys are in Ms. Jones' class; that fraction would be (5/8)(3/7), or 15/56. This 15/56 represents the fraction of the entire sixth grade class who are in Ms. Jones' class.
Answer:
<h2>m∠ABD = 20°</h2>
Step-by-step explanation:
If m∠ABC = 40° and BD is the bisector of ∠ABC, then
(1) m∠ABD = m∠DBC
(2) m∠ABC = m∠ABD + m∠DBC
From (1) and (2) we have:
m∠ABC = 2m∠ABD
Therefore
2m∠ABD = 40° <em>divide both sides by 2</em>
m∠ABD = 20°
