Advertisements
Advertisements
Question
In the given figure, if AE || DC and AB = AC, the value of ∠ABD is
Options
70°
110°
120°
130°
Advertisements
Solution
We have to find the value of ∠ABD in the following figure.
It is given that
∠MAE = 70°
∠NAC = 70°(Vertically apposite angle)
Now ∠MAE + ∠EAB + ∠BAC =180° (linear pair) …… (1)
Similarly ∠EAB +∠BAC +∠NAC = 180° (linear pair) …… (2)
From equation (1) we have
∠EAB + ∠BAC = 180°
= 110°
Now ∠FCA = ∠DBA (same exterior angle)
∠ACF = ∠EAC (Interior angle)
Now
∠EAC = 110°
So ∠AFC = 110°
Since ∠AFC =∠ABD
Hence (b)∠ABD = 110°.
APPEARS IN
RELATED QUESTIONS
In triangles ABC and PQR, if ∠A = ∠R, ∠B = ∠P and AB = RP, then which one of the following congruence conditions applies:
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle is
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
In the following figure, OA = OC and AB = BC.
Prove that:
(i) ∠AOB = 90o
(ii) ΔAOD ≅ ΔCOD
(iii) AD = CD
The following figure shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that:
State, whether the pairs of triangles given in the following figures are congruent or not:
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
In the figure, BM and DN are both perpendiculars on AC and BM = DN. Prove that AC bisects BD.
AD and BE are altitudes of an isosceles triangle ABC with AC = BC. Prove that AE = BD.
“If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent.” Is the statement true? Why?
