Advertisements
Advertisements
Question
In parallelogram LOST, SN ⊥ OL and SM ⊥ LT. Find ∠STM, ∠SON and ∠NSM.
Advertisements
Solution
Given, ∠MST = 40°
In ΔMST,
By the angle sum property of a triangle,
∠TMS + ∠MST + ∠STM = 180°
⇒ ∠STM = 180° – (90° + 40°) ...[∵ SM ⊥ LT, ∠TMS = 90°]
= 50°
∴ ∠SON = ∠STM = 50° ...[∵ Opposite angles of a parallelogram are equal]
Now, In the ΔONS,
∠ONS + ∠OSN + ∠SON = 180° ...[Angle sum property of triangle]
∠OSN = 180° – (90° + 50°)
= 180° – 140°
= 40°
Moreover, ∠SON + ∠TSO = 180° ...[∵ Adjacent angles of a parallelogram are supplementary]
⇒ ∠SON + ∠TSM + ∠NSM + ∠OSN = 180°
⇒ 50° + 40° + ∠NSM + 40° = 180°
⇒ 90° + 40° + ∠NSM = 180°
⇒ 130° + ∠NSM = 180°
⇒ ∠NSM = 180° – 130° = 50°
APPEARS IN
RELATED QUESTIONS
Consider the given parallelograms. Find the values of the unknowns x, y, z.
In the given figure, G is the point of concurrence of medians of ΔDEF. Take point H on ray DG such that D-G-H and DG = GH, then prove that `square`GEHF is a parallelogram.
In the adjacent figure, if seg AB || seg PQ, seg AB ≅ seg PQ, seg AC || seg PR, seg AC ≅ seg PR then prove that, seg BC || seg QR and seg BC ≅ seg QR.
Construct ☐ BARC such that l(BA) = l(BC) = 4.2 cm, l(AC) = 6.0 cm, l(AR) = l(CR) = 5.6 cm
In parallelogram ABCD, ∠A = 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram, if AB = 5x – 7 and CD = 3x +1 ; find the length of CD.
PQRS is a parallelogram whose diagonals intersect at M.
If ∠PMS = 54°, ∠QSR = 25° and ∠SQR = 30° ; find :
(i) ∠RPS
(ii) ∠PRS
(iii) ∠PSR.
In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.
Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between b and c
Which of the following figures satisfy the following properties?
- All sides are congruent.
- All angles are right angles.
- Opposite sides are parallel.
In the following figure, FD || BC || AE and AC || ED. Find the value of x.
