in the diagram abc is a straight line. ad is parallel to be, angle bad =34 and ab=db
Answers
a. p = 34° because ΔABD is an isosceles triangle.
q = 34° because alternative interior angles.
b. r = 112° and s = 56°
c. t = 34° because straight line has angle of 180°
Given that,
In the diagram ABC is a straight line.
AD is parallel to BE (AD ║ DE)
Angles ∠BAD =34 and AB = DB
We have to find the values of p, q, r, s and t with the reasons.
We know that,
From triangle ΔABD is an isosceles triangle because the two sides are equal that are AB = BD then the angle ∠BAD = ∠ADB
34° = p
p = 34°
From parallel lines AD ║ BE because alternative interior angles
∠ADB = ∠DBE
p = q
q = 34°
From ΔABD because sum of the angles of the triangle is 180°.
34° + p + r = 180°
34° + 34° + r = 180°
r = 180° - 68°
r = 112°
From ΔBDE because right angle triangle sum of the angles of the triangle is 180°.
90° + q + s = 180°
90° + 34° + s = 180°
s = 180° - 124°
s = 56°
From the straight line at point B the angles are r,q and t
Angles on the straight line is 180°.
r + q + t = 180°
112° + 34° + t = 180°
t = 180 - 146
t = 34°
Therefore, The angles are ∠p = 34°, ∠q = 34°, ∠r = 112°, ∠s = 56° and ∠t = 34°.
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