Question

i) In a ΔABC, ∠A =500

, ∠B = 600

and ∠C = 700

. Find the measures of the

angles of the triangle formed by joining the mid-points of the sides of this

triangle.

(ii)The angle between two altitudes of a parallelogram through the vertex of

an obtuse angle of the parallelogram is 50°. Find the angles of the

parallelogram.
​

Answer 1

Step-by-step explanation:

Given-

□ABCD is a parallelogram.

∠B & ∠D are obtuse.

BM & DN are altitudes from B & D on AD & AB, respectively, intersecting at O.

∠DOM=BON ...(vertically opposite angles=60⁰ )

To find out-

The angles of the parallelogram ABCD.

Solution-

∠DOM+∠NOM=180⁰ ...(linear pair)

⟹60⁰+∠NOM=180⁰

⟹∠NOM=120⁰........(i)

Now, ∠AMO=∠DNO=90⁰

...(both are perpendiculares on AD & AB, respectively.)$$

∴ In the quadrilateral AMON,

∠AMO+∠DNO=180⁰

∴∠NOM+∠MAN=360⁰−180⁰

=180⁰

(sum of the angles of a quadrilateral =360⁰)

⟹∠MAN=180⁰

−120⁰

...(from i )

i.e ∠A=60

∴∠A=∠C=60⁰

....(opposite angles of a paralleogram)

∴∠D+∠B=360⁰ −120⁰ =240⁰

∴∠D=∠B=2 240⁰ =120⁰

...(opposite angles of a paralleogram)

Ans- ∠A=∠C=60⁰,∠D=∠B=120⁰

xXitzSweetMelodyXx

Answer 2

Answer:

.4casesperhourbecause

8

3

equals.4