Question

the measure of two angles are 42 degree and 90 degree find the third angle​

Answer 1

DIAGRAM :

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5)\put(2.8,.3)\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf 42 }\end{picture}$

Given : Measure of the two angles of a triangle are 42° and 90°.

To Find : Third angle of the triangle.

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Here, two angles of a triangle are given as 42° and 90°. We've to find the third angle of the triangle. As , we know that sum of all angles of a triangle is 180°, i.e.

$\: \:$

$\star \: \underline{\boxed{\sf\pink{ \angle \: A + \angle \: B + \angle \:C = 180 \degree }}}$

$\: \:$

By putting the values, we get,

$\: \:$

$\sf:\implies \: \angle \: A \: + \angle \: B + \angle \:C = 180 \degree \\ \\ \\ \sf:\implies \: \angle \: A + 90 \degree + 42 \degree = 180 \degree \\ \\ \\ \sf:\implies \: \angle \: A + 132 \degree = 180 \degree \\ \\ \\ \sf:\implies \: \angle \: A = 180 \degree - 132 \degree \\ \\ \\ \sf:\implies \:\: \underline{\boxed{\mathfrak\purple{ \angle \:A = 48 \degree }}} \bigstar \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \:third \: angle \: of \: the \: triangle \: is \: \bold{48 \degree}.}}$

Answer 2

Answer:

Given:

» Measures of two angles of triangle are 42⁰ and 90⁰.

To find:

» The third angle of the triangle.

Solution:

Let third angle be x.

• Sum of all angles of triangle is 180⁰.

» 42⁰ + 90⁰ + x = 180⁰

» x = 180⁰ - 132⁰

» x = 48⁰

Therefore, the third angle of the triangle is 48⁰.