If a triangle has two angles that measure 45 and 90 degrees, what is the measure of the third angle?
Let the measure of the third angle be x.
We know that the sum of all interior angles of a triangle is 180°.
∴ ∠a + ∠b + ∠c = 180°
⇒45 + 90 + x = 180
⇒135 + x = 180
⇒x = 180 - 135
⇒x = 45
[ The value of x is 45° ]
∴ ∠a + ∠b + ∠c = 180°
⇒45 + 90 + x = 180
⇒45 + 90 + 45 = 180
⇒90 + 90 = 180
⇒180 = 180
The measurement of the third angle is 45° so option B. 45° will be the correct answer.
Let other angle be x
Using Angle sum property
[tex]\\ \sf\longmapsto x+45+90=180[/tex]
[tex]\\ \sf\longmapsto x+135=180[/tex]
[tex]\\ \sf\longmapsto x=180-135[/tex]
[tex]\\ \sf\longmapsto x=45°[/tex]
option B