In △ABC, BD ⟂ AC at D and ∠DBC = 14°. E is a point on BC such that ∠CAE = 75°. What is the measure of ∠AEB?
Given
BD is perpendicular to AC at D ()
Formula Used
Sum of angles in a triangle =
Angles on a straight line add up to
Solution
In right-angled triangle BDC, the sum of angles is
In triangle AEC, the sum of angles is
Since points B, E, and C lie on a straight line, angles AEB and AEC are a linear pair.
Final Answer
So the correct answer is (b)
English
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90 Mins English English100 Questions100 Marks90 Mins English English100 Questions100 Marks90 Mins EnglishWhich of the following is not a pythagorian triplet?
In △ABC, BD ⟂ AC at D and ∠DBC = 14°. E is a point on BC such that ∠CAE = 75°. What is the measure of ∠AEB?
If the angles of a triangle are 4x°, 3x°, 2x° then 1/4x° =
If the sides of a triangle are in the ratio of 1:√3:2, then what is the ratio of its corresponding angles ?
In △ABC, AB = AC = 12 cm, BC = 5 cm and D is a point on AC such that DB = BC. What is the measure of CD?
In a triangle ABC, medians AD and BE intersect at G. If the length of median AD is 12 cm, what is the length of the segment AG?
In △ABC, BD ⟂ AC at D and ∠DBC = 25°. E is a point on BC such that ∠CAE = 80°. What is the measure of ∠AEB?
The number of possible triangles with any three of the lengths 1.2 cm, 4.2 cm, 5.9 cm, and 8.1 cm is:
In △ABC, BD ⟂ AC at D and ∠DBC = 22°. E is a point on BC such that ∠CAE = 36°. What is the measure of ∠AEB?
In △LMN, medians MX and NY are perpendicular to each other and intersect at Z. If MX = 20 cm and NY = 30 cm, what is the area of △LMN (in cm²)?
Suggested Test Series
Suggested Test Series
Which of the following is not a pythagorian triplet?
In △ABC, BD ⟂ AC at D and ∠DBC = 14°. E is a point on BC such that ∠CAE = 75°. What is the measure of ∠AEB?
If the angles of a triangle are 4x°, 3x°, 2x° then 1/4x° =
If the sides of a triangle are in the ratio of 1:√3:2, then what is the ratio of its corresponding angles ?
In △ABC, AB = AC = 12 cm, BC = 5 cm and D is a point on AC such that DB = BC. What is the measure of CD?
In a triangle ABC, medians AD and BE intersect at G. If the length of median AD is 12 cm, what is the length of the segment AG?
In △ABC, BD ⟂ AC at D and ∠DBC = 25°. E is a point on BC such that ∠CAE = 80°. What is the measure of ∠AEB?
The number of possible triangles with any three of the lengths 1.2 cm, 4.2 cm, 5.9 cm, and 8.1 cm is:
In △ABC, BD ⟂ AC at D and ∠DBC = 22°. E is a point on BC such that ∠CAE = 36°. What is the measure of ∠AEB?
In △LMN, medians MX and NY are perpendicular to each other and intersect at Z. If MX = 20 cm and NY = 30 cm, what is the area of △LMN (in cm²)?
