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?
Given:
In △ABC, BD ⟂ AC at D and ∠DBC = 22°. E is a point on BC such that ∠CAE = 36°.
Formula Used:
Sum of angles in a △ = 180°.
Solution:
In △BDC, since BD ⟂ AC:
∠BDC = 90°.
We have, ∠DBC = 22°.
Then, ∠BDC + ∠DCB + ∠DBC = 180°
90° + ∠DCB + 22° = 180°
∠DCB = 180° − 112°
∠DCB = 68°.
In △AEC, ∠CAE = 36°.
Then, ∠AEB = ∠CAE + ∠DCB
∠AEB = 36° + 68°
∠AEB = 104°.
English
100 Questions
100 Marks
90 Mins English English100 Questions100 Marks90 Mins English English40 Questions30 Marks25 Mins EnglishIn △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?
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)?
The value of x in the given diagram is
In an isosceles triangle, the vertex angle measures 76°. What is the measure of each ofthe base angles?
In PQR, 3 P = 4Q = 6R, then find the value of ().
Suggested Test Series
Suggested Test Series
