Question

In the given figure, $l ‖ m$ and a transversal $t$ cuts them. If $∠ 1 : ∠ 2 = 2 : 3,$ find the measure of each of the marked angles.

Accepted Answer

Given, $l ‖ m$ and a transversal $t$ cuts them.

Also given, $∠ 1 : ∠ 2 = 2 : 3$

So, $∠ 1 = 2 x$ and $∠ 2 = 3 x$

From the given figure, we know that $∠ 1$ and $∠ 2$ form a linear pair of angles.

Therefore, $∠ 1 + ∠ 2 = 180 °$

$\Rightarrow 2 x + 3 x = 180 °$

$\Rightarrow 5 x = 180 °$

$\Rightarrow x = 36 °$

By substituting the value of $x$ , we get

$∠ 1 = 2 x = 2 \times (36 °) = 72 °$

$∠ 2 = 3 x = 3 \times (36 °) = 108 °$

Since $l ∥ m$ and $t$ is a transversal then $∠ 1$ and $∠ 3$ form alternate interior opposite angles.

We know that, alternate interior angles are always equal.

$\Rightarrow$ $∠ 1 = ∠ 3 = 72 °$

From the figure we know that $∠ 2$ and $∠ 4$ form alternate interior opposite angles.

$\Rightarrow$ $∠ 2 = ∠ 4 = 108 °$

It is given that, $l ∥ m$ and $t$ is a transversal.

We know that, the corresponding angles are always equal.

So the corresponding angles according to the figure is written as

$∠ 1 = ∠ 5 = 72 °$

$∠ 2 = ∠ 6 = 108 °$

$∠ 3 = ∠ 7 = 72 °$

$∠ 4 = ∠ 8 = 108 °$

Thus, the required solution is obtained.

R S Aggarwal and Veena Aggarwal Solutions for Exercise 3: EXERCISE 7C

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal and Veena Aggarwal Solutions for Exercise 3: EXERCISE 7C

Questions from R S Aggarwal and Veena Aggarwal Solutions for Exercise 3: EXERCISE 7C with Hints & Solutions

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