Ex.3.3 Q7 Understanding Quadrilaterals Solution-Ncert Maths Class 8

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Question

The adjacent figure \(HOPE\) is a parallelogram. Find the angle measures \(x, y\) and \( z.\) State the properties you use to find them.

Text Solution

What is Known?

Given figure is a parallelogram.

What is Unknown?

Values of \(x, y, z.\)

Reasoning:

In a parallelogram, opposite angles are equal and adjacent angles are supplementary. Using this property, we can calculate the unknown angles.

Steps:

Here,

\[\begin{align}\angle &{\rm{HOP }} + {\rm{ 7}}0^\circ = {\rm{ 18}}0^\circ {\rm{ }}\,\,\left[ {{\text{Angles of linear pair}}} \right]\\\angle &{\rm{HOP}} = {\rm{18}}0^\circ - {\rm{7}}0^\circ \\\angle &{\rm{HOP}} = {\rm{11}}0^\circ \\\angle &{\rm{O }} = \angle E\left( {{\text{opposite angles are equal}}} \right)\\\therefore &{\rm{x}} = {\rm{11}}0^\circ {\rm{ }}\end{align}\]

\[\begin{align}\text{y}&={{40}^{\text{o}}}\text{ (Alternate interior angles are equal) }  \\
\text{z}+{{40}^{\circ}}&={{70}^{\circ}}\text{ (Corresponding angles) }  \\ \text{z}&={{70}^{\circ}}-{{40}^{\circ}}  \\ \text{z}&={{30}^{\circ}} \\ \end{align}\]

\[\therefore {\text{ x }} = {\rm{ 11}}0^\circ ,{\text{ y }} = {\text{ 4}}0^\circ ,{\rm{ z }} = {\text{ 3}}0^\circ \]