In a rhombus mpkn with an obtuse angle k the diagonals intersect each other at point e. the measure of one of the angles of a triangle pke is equal 16°. find the measures of the other angles of this triangle and the measures of the angles of triangle pmn. m∠kep = m∠ekp = m∠n pm= m∠m = m∠mnp =

m∠KEP=90°,  m∠NPM=16°, m∠KPE=16° , m∠EKP=74°, m∠PMN=148°, m∠MNP=16°

Step-by-step explanation:

Given In a rhombus MPKN with an obtuse angle K the diagonals intersect each other at point E.

The measure of one of the angles of a triangle PKE is equal 16°. we know diagonals of rhombus bisect at right angles i.e at 90°

Hence, m∠KEP=90°

As ∠K is given as obtuse angles so the only possible angle which measures 16° in triangle PKE is ∠KPE. Hence, m∠KPE=16°

In triangle KEP, by angle sum property

m∠EKP+m∠KEP+m∠KPE=180°

⇒ m∠EKP+90°+16°=180°

⇒ m∠EKP=74°

∵ The diagonals bisect the angles at vertices of rhombus.

⇒ ∠NPK=∠NPM=16°

and ∠PKN=2(∠PKE)=2(74°)=148°

∵ Opposite angles of rhombus are equal

⇒ ∠PKN=∠PMN=148°

In triangle PMN, By angle sum property

m∠NPM+m∠PMN+m∠MNP=180°

⇒ 16°+148°+m∠MNP=180°

⇒ m∠MNP=16°

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is