Question

one of the angles of a triangle PQR is 80degree and the other two angles are equal. find the measure

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Answer 1

Given :-

• One of the angles of a triangle PQR is 80° and the other two angles are equal.

To Find :-

• The measure of remaining two angles.

Solution :-

Since,we are given that the other two angles are equal. So,we can assume both of them as x.

In any given traingle, the sum of measure of three angles must be equal to 180°.

Therefore,for a ∆PQR :

→ x + x + 80° = 180° (Angle sum property of ∆)

→ 2x + 80° = 180°

→ 2x = 180 - 80

→ 2x = 100

→ x = 100 ÷ 2

→ x = 50°

Therefore,the measure of remaining two angles is 50°.

___________________

More to know : -

• If you have one angle given, then the sum of the other two angles will be equal to 180 - measure of the given angle.

• If you have two angles given, then the measure of the third angle will be equal to 180 - the sum of the other two angles.

Answer 2

$\huge\bold{\mathbb{QUESTION}}$

one of the angles of a triangle PQR is $80°$ and the other two angles are equal. find the measure of the other two angles.

$\huge\bold{\mathbb{GIVEN}}$

• One of the angles of a triangle PQR is $80°.$

• The other two angles are equal.

$\huge\bold{\mathbb{TO\:FIND}}$

The measure of the other two angles.

$\huge\bold{\mathbb{DIAGRAM}}$

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf P }\put(0.5,-0.3){ \bf Q }\put(5.2,-0.3){ \bf R }\end{picture}$

$\huge\bold{\mathbb{SOLUTION}}$

Since the other two angles are equal, let the measure of each of them be $x°.$

We know that:

Sum of all angles of a triangle is $180°.$

So, we can say-

$x + x + 80 = 180$

$\implies 2x+80 = 180$

$\implies 2x = 180-80$

$\implies 2x = 100$

$\implies x = {\Large{\frac{100}{2}}}$

$\implies x = 50$

$\huge\bold{\mathbb{HENCE}}$

$x = 50$

Measure of each of the two angles

$=x° = 50°$

$\huge\bold{\mathbb{THEREFORE}}$

The measure of each of the two equal angles is $50°.$

$\huge\bold{\mathbb{DONE}}$