Question

If a triangle has two angles that measure 45 and 90 degrees, what is the measure of the third angle?

A. 90

B. 45°

C. 60

D. 30

Answer 1

Problem:-

If a triangle has two angles that measure 45 and 90 degrees, what is the measure of the third angle?

Solution:-

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° ]

Verification:-

∴ ∠a + ∠b + ∠c = 180°

⇒45 + 90 + x = 180

⇒45 + 90 + 45 = 180

⇒90 + 90 = 180

⇒180 = 180

Answer:-

The measurement of the third angle is 45° so option B. 45° will be the correct answer.

〜Hope it's helpful!

Answer 2

Let other angle be x

Using Angle sum property

$\\ \sf\longmapsto x+45+90=180$

$\\ \sf\longmapsto x+135=180$

$\\ \sf\longmapsto x=180-135$

$\\ \sf\longmapsto x=45°$

option B