Question

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

Answer 1

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

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.

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

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

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 $50°.$

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

Answer 2

Let other angles be = x, y

Given that: x = y

By Angle Sum Property of ∆:-

→ 80 + x + x = 180

→ 2x = 100

→ x = 50°