In quadrilateral PQRS,M is the foot of perpendicular from S to line PQ If m angle PSM= 10 Find two - Maths - Quadrilaterals

Question

In quadrilateral PQRS,M is the foot of perpendicular from S to line
PQ If m angle PSM= 10 Find two possible measures of angle P of
quadrilateral PQRS i want direct ans pl no links

Diksha Verma · Accepted Answer

Given: In quadrilateral PQRS, M is the foot of perpendicular from s
to line PQ and ∠PSM=10°As shown in above figure, The first
possible measures of ∠p of quadrilateral,In ∆PSM,
∠PMS=90°, ∠PSM=10°
∠p+∠PMS+∠PSM=180° (As we know, sum of all angle of
triangle is
180°)∠p+90°+10°=180°∠p=180°-100°∠p=80°
AnsThe second possible measures of ∠p of quadrilateral,In
quadrilateral MQRS, ∠QMS=90°, ∠MSR=∠s,
∠SRQ=∠r, ∠RQM=∠q i e
90°+∠s+∠r+∠q=360° (As we know, sum of all angle
of quadrilateral is 360°)⇒ ∠s+∠r+∠q=270°
(1)Now in quadrilateral
PQRS,∠p+(∠s+10°)+∠r+∠q=360°∠p+∠s+∠r+∠q=350°from
equation (1),∠p+270°=360°∠p=80° Ans

In quadrilateral PQRS,M is the foot of perpendicular from S to line PQ.If m angle PSM= 10.Find two possible measures of angle P of quadrilateral PQRS.i want direct ans pl.no links