Tile 1:In any triangle (regardless its type), the sum of measures of the internal angles is 180°.
This means that:
∠ABC + ∠BAC + ∠ACB = 180°
Tile 2:The sum of measures of internal angles of a triangle is 180°.
We are given that:
ΔABC is isosceles where AB = AC
This means that:
∠ABC = ∠ACB
We are also given that measure angle BAC is 70 degrees
180 = ∠ABC + ∠ACB + 70
∠ABC + ∠ACB = 110°
We know that both angles are equal, therefore:
∠ABC = ∠ACB = 110/2 = 55°
Tile 3:We are given that ΔQPR is an isosceles triangle where PQ = QR
This means that:
∠QPR = ∠QRP
We are given that ∠QRP = 30°
This means that:
∠QPR = 30°
Tile 4:A diagram representing the given scenario is attached.
Now we have:
point D is midpoint to AB and point E is midpoint to BC
There is a theorem stating that: "In a triangle, a line joining the midpoints of two sides is parallel to the third side and equals half its length"
Applying this to the givens, we would conclude that:
ED is parallel to AC
Now, since these two lines are parallel, then angles BAC and BDE are corresponding angles which means that they are equal.
This means that:
∠BAC = ∠BDE = 45°
Hope this helps :)
Answer:
48
Step-by-step explanation:
<h2>Answer:</h2>
This is a theorem called Converse of Alternate Exterior Angles that states that <em>if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel</em>. Moreover, this theorem is based upon the corresponding Angles Converse Postulate that states that<em> if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. </em>We don't need to prove this postulate, it's assume to be true. So our goal is to get corresponding angles congruent in order to use the corresponding Angles Converse Postulate,
1.
Reason: Given
Statement:
2.
Reason: Def of vertical
Statement:
3.
Reason: Def of vertical
Statement:
4.
Reason: Transitive Property
Statement:
5.
Reason: corresponding Angles Converse Postulate
Statement:
Is there options for this question? I dont understand what your asking.
Well I think they are approximately the same I'm not exactly sure but they are close to each other