The degree measures of three angles of a triangle are x, y and z. If then find the value of z. - Wired Faculty

Lines And Angles

Question

The degree measures of three angles of a triangle are x, y and z. If $straight z equals fraction numerator straight x plus straight y over denominator 2 end fraction comma$ then find the value of z.

Solution

∵ x, y and z are the degree measures of three angles of a triangle
∴ x + y + z = 180°
| Angle sum property of a triangle
$rightwards double arrow space space space space fraction numerator straight x plus straight y over denominator 2 end fraction plus straight z over 2 equals 90 degree$
| Dividing throughout by 2
$rightwards double arrow space space straight z plus straight z over 2 equals 90 degree space space space space space space space space space space space space space space space space space vertical line space because space straight z equals fraction numerator straight x plus straight y over denominator 2 end fraction rightwards double arrow space space space fraction numerator 3 straight z over denominator 2 end fraction equals 90 degree rightwards double arrow space space space space straight z equals 2 over 3 left parenthesis 90 degree right parenthesis rightwards double arrow space space space space straight z space equals space 60 degree$

Some More Questions From Lines and Angles Chapter

For Daily Free Study Material Join wiredfaculty

Lines And Angles

The degree measures of three angles of a triangle are x, y and z. If $straight z equals fraction numerator straight x plus straight y over denominator 2 end fraction comma$ then find the value of z.

Some More Questions From Lines and Angles Chapter

Rays OA, OB. OC, OD and OE have the common initial point O. Show that ∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA = 360°.

Prove “if two lines intersect each other, then the vertically opposite angles are equal.”

In figure, OP bisects ∠AOC, OQ bisects ∠BOC and OP ⊥ OQ. Show that the points A, O and B are collinear.

In figure, if y = 20°, prove that the line AOB is a straight line.

In the given figure, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex angle EOC.

In figure, lines PQ and RS intersect each other at point O. If ∠POR : ∠ROQ = 5 : 7, find all the angles.

In figure, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠SOQ, respectively. If ∠POS = x, find ∠ROT.

If the complement of an angle is one-third of its supplement, find the angle.

In figure, find the value of x.

In figure, if ∠POR and ∠QOR form a linear pair and a - b = 80° then find the value of a and b.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction