Question Video: Finding the Measure of an Angle in an Isosceles Triangle given the Measure of Its Vertex Angle | Nagwa Question Video: Finding the Measure of an Angle in an Isosceles Triangle given the Measure of Its Vertex Angle | Nagwa

# Question Video: Finding the Measure of an Angle in an Isosceles Triangle given the Measure of Its Vertex Angle Mathematics • Second Year of Preparatory School

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In the displayed model of a house, what angle does the roof make with the horizontal, given that Ξπ΄πΈπ΅ is isosceles?

02:17

### Video Transcript

In the displayed model of a house, what angle does the roof make with the horizontal, given that triangle π΄πΈπ΅ is isosceles?

Itβs probably most useful to begin this question by highlighting the triangle π΄πΈπ΅ that we want to consider. This triangle forms the roof of this house, and weβre told that itβs isosceles. We should recall that in an isosceles triangle, we have two sides equal in length and two base angles are equal. So in this diagram, the side π΄πΈ is equal to the side π΄π΅ and the angle π΄πΈπ΅ is equal to the angle π΄π΅πΈ.

Now that weβve had a look at the diagram, letβs focus on what weβre asked, to find the angle that the roof makes with the horizontal. That means that weβre really looking for the angle created by the slope of the roof and the horizontal axis. Either of the two base angles would give us the answer for this. So letβs see if we can work out one of these angles, angle π΄π΅πΈ.

In order to do this, weβll need to remember an important fact about the angles in a triangle. And that is that the angles in a triangle add up to 180 degrees. This means that we can write that angle π΅π΄πΈ plus angle π΄πΈπ΅ plus angle π΄π΅πΈ is equal to 180 degrees. Weβre given that angle π΅π΄πΈ is 107 degrees. So if we subtract 107 degrees from both sides of this equation, we get that angle π΄πΈπ΅ plus angle π΄π΅πΈ is equal to 73 degrees. As we have an isosceles triangle, we know that our two base angles are equal. So angle π΄πΈπ΅ is equal to angle π΄π΅πΈ.

We could think of this then that two times angle π΄π΅πΈ is 73 degrees. And so to find angle π΄π΅πΈ, we must divide both sides of this equation by two, which means that the measure of angle π΄π΅πΈ is 36.5 degrees as a decimal. We can therefore give our answer that the angle that the roof makes with the horizontal is 36.5 degrees.

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