Question

In the figure above, if $l$ || $m$ and $r={91}^o$, then $t+u=$

• A. ${178}^o$
• B. ${179}^o$
• C. ${180}^o$
• D. ${181}^o$
• E. ${182}^o$

Answer 1

The correct option is A ${178}^o$

Given, $l$ $||$ $m$

Sum of the angles in a straight line $=$ ${180}^o$

Here, $r$ $+$ $s$ $=$ ${180}^o$

As $r$ $=$ ${91}^o$,

$\Rightarrow {91}^o$ $+$ $s$ $=$ ${180}^o$

$\Rightarrow s$ $=$ ${180}^o$ $-$ ${91}^o$

$\Rightarrow s$ $=$ ${89}^o$

When two lines are parallel, corresponding angles are equal.

From the given figure,

$s$ and $u$ are corresponding angles.

$s$ $=$ $u$

$s$ $=$ $u$ $=$ ${89}^o$

Vertically opposite angles are equal.

Here, $u$ and $t$ are vertically opposite angles

$u$ $=$ $t$

$u$ $=$ $t$ $=$ ${89}^o$

$t$ $+$ $u$ $=$ ${89}^o$ $+$ ${89}^o$

$t+u=$ ${178}^o$

Therefore, the value of $(t$ $+$ $u)$ is ${178}^o$.