In the adjacent figure `bar(OP) , bar(OQ) , bar(OR)` and`bar(OS)` are four rays. Prove that
`anglePOQ+angleQOR+angleSOR+anglePOS=360^(@)` .

In the adjacent figure, bar(AB) is a straight line. Find the value of x and also find angleAOC, angleCOD and angleBOD .

In the given figure bar(PQ) is a line. Ray bar(OR) is perpendicular to line bar(PQ) . bar(OS) is another ray lying between rays bar(OP) and bar(OR) . Prove that angleROS = (1)/(2) angleQOS − anglePOS

In the adjacent figure ray OS stands on a line PQ. Ray OR and ray OT are angle bisectors of anglePOS and angleSOQ respectively. Find angleROT .

In the given figure lines bar(AB) and bar(CD ) intersect at O. If angleAOC+ angleBOE= 70^(@) and angleBOD = 40^(@) , find angleBOE and reflex angleCOE .

In the given figure AS || BT, angle4 = angle5 bar(SB) bisects angleAST . Find the measure of angle1

In the given figure three lines bar(AB) , bar(CD) and bar(EF) intersecting at O. Find the values of x, y and z it is being given that x : y : z = 2 : 3 : 5

In the given figure lines bar(XY) and bar(MN) intersect at O. If ∠POY = 90^(@) and a: b = 2 : 3, find c.

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that bar(OP)*bar(OQ)+bar(OR)*bar(OS)=bar(OR)*bar(OP)+bar(OQ)*bar(OS)=bar(OQ)*bar(OR)+bar(OP)*bar(OS) Then the triangle PQR has S as its

Given that bar(x) is the mean and sigma^(2) is the variance of n observation x_(1), x_(2), …x_(n). Prove that the mean and sigma^(2) is the variance of n observations ax_(1),ax_(2), ax_(3),….ax_(n) are abar(x) and a^(2)sigma^(2) , respectively, (ane0) .

Prove the following properties: Re(z) = (z + bar(z))/(2) and Im(z) = (z - bar(z))/(2i)