Q31 of 34 Page 252

In the given figure, in a ΔABC, BE ⊥ AC, ∠EBC = 40° and ∠DAC = 30. ∠DAC = 30°. Find the values of x, y and z.

We know that,

Sum of all angles in a triangle = 180°


So, in ΔBEC


= 40 + x + 90 = 180


So, x = 50°


Now, in ΔADC-


= 50 + 30 + ∠ADC = 180


= ∠ADC = 100°


Since BC represents a straight line, sum of angles = 180°.


So, ∠ADC + y = 180


hence y = 80° since ∠ADC = 100°


By exterior angle sum theorem of the smaller triangle formed-


z = ∠DAE + ∠BEA = 90° + 30° = 120°


More from this chapter

All 34 →
29

Prove that: (a + b)3 + (b + c)3 + (c + a)3 - 3(a + b)(b + c)(c + a) = 2(a3 + b3 + c3 - 3abc)

 30

On a graph paper plot the following points:

A(3, 3), B(2, 4), C(5, 5), D(0, 2), E(3, -3) and F(-5, -5).


Which of these points are the mirror images in (i) x-axis (ii) y-axis?

 32

In the given figure, ABC is a triangle in which AB = AC. D is a point in the interior of ΔABC such that ∠DBC = ∠DCB. Prove that AD bisects ∠BAC.

 33

In the given figure, ABCD is a square and EF is parallel to diagonal DB and EM = FM. Prove that: (i) BF = DE (ii) AM bisects ∠BAD.