In Fig. 6.13, ∠BAC = 90°, AD ⊥ BC and ∠BAD = 50°, then ∠ACD is
a. 50°
b. 40°
c. 70°
d. 60°
Solution:
Given, ABC is a triangle
Also, ∠BAC = 90°, AD ⊥ BC and ∠BAD = 50°
We have to find the measure of ∠ACD.
By angle sum property of a triangle,
We know that the sum of all the three interior angles of the triangle is equal to 180 degrees.
Considering triangle ABD,
∠ADB + ∠ABD + ∠BAD = 180°
90° + ∠ABD + 50° = 180°
∠ABD + 140° = 180°
∠ABD = 180° - 140°
∠ABD = 40°
Considering triangle ABC,
∠BAC + ∠BCA + ∠ABC = 180°
90° + ∠BCA + 40° = 180°
∠BCA + 130° = 180°
∠BCA = 180° - 130°
∠BCA = 50°
We observe that ∠BCA = ∠ACD
Therefore, ∠ACD = 50°
✦ Try This: In Fig. 4.58, ΔABC is a triangle such that AB/AC =BD/DC, ∠B = 70°, ∠C = 50°. Find ∠BAD
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 24
In Fig. 6.13, ∠BAC = 90°, AD ⊥ BC and ∠BAD = 50°, then ∠ACD is: a. 50°, b. 40°, c. 70°, d. 60°
Summary:
In Fig. 6.13, ∠BAC = 90°, AD ⊥ BC and ∠BAD = 50°, then ∠ACD is 50°
☛ Related Questions:
- If one angle of a triangle is equal to the sum of the other two angles, the triangle is: a. Obtuse, . . . .
- In Fig. 6.12, PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°, then the measure of . . . .
- In Fig. 6.11, the value of ∠A + ∠B + ∠C + ∠D + ∠E + ∠F is: a. 190°, b. 540°, c. 360°, d. 180°