In the roof truss shown, AB=8 and m∠HAF=37∘. Find: m∠ADB Given: AB=8 and m∠HAF=37∘. The roof truss has line symmetry. Figure(1)

Approach: The sum of measure of three angles in a triangle is 180∘. Calculation: Equate the sum of measure of three angles of the triangle to 180∘. m∠BAD+m∠ABD+m∠ADB=180∘.. (1) Substitute 37∘ for m∠BAD and 90∘ for m∠ABD in equation (1) in order to find the value of m∠ADB. 37∘+90∘+m∠ADB=180∘ m∠ADB=180∘—37∘—90∘ =53∘ Therefore, the value of m∠ADB is 53∘. Conclusion: The value of m∠ADB is 53∘.

Question: "In the roof truss shown, AB=8 and m∠HAF=37∘...."

High School
Geometry
High school geometry
Congruence

Tyra

Answered question

2021-07-27

In the roof truss shown, AB=8 and

m ∠ H A F = 37^{\circ}

.
Find:

m ∠ A D B

Given:
AB=8 and

m ∠ H A F = 37^{\circ}

.
The roof truss has line symmetry.

Figure(1)

Answer & Explanation

Yusuf Keller

Skilled2021-07-28Added 90 answers

Approach:
The sum of measure of three angles in a triangle is

180^{\circ}

.
Calculation:
Equate the sum of measure of three angles of the triangle to

180^{\circ}

m ∠ B A D + m ∠ A B D + m ∠ A D B = 180^{\circ}

.. (1)
Substitute

37^{\circ}

for

m ∠ B A D

and

90^{\circ}

for

m ∠ A B D

in equation (1) in order to find the value of

m ∠ A D B

37^{\circ} + 90^{\circ} + m ∠ A D B = 180^{\circ}

m ∠ A D B = 180^{\circ} — 37^{\circ} — 90^{\circ}

= 53^{\circ}

Therefore, the value of

m ∠ A D B

53^{\circ}

.
Conclusion:
The value of

m ∠ A D B

53^{\circ}

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